Thermodynamic Lattice Study for Preconformal Dynamics in Strongly - - PowerPoint PPT Presentation

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavored QCD-Like Theory

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB, A. DeuzemanC, and T. SilvaB

Laboratori Nazionali di Frascati - INFNA Rijksuniversiteit GroningenB University of BernC

Talk at KMI-SCGT, Nagoya Univ. Dec. 04, 2012 Reference

• K. Miura, M. P. Lombardo and E. Pallante, Phys. Lett. B 710 (2012) 676.
• K. Miura, M. P. Lombardo and E. Pallante, PoS Lattice 2011, arXiv:1111.1098 [hep-lat].

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

QCD: Negative Beta-Func.

Nf 3

QCD

g beta anti-screening > screening

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

Loss of Asymptotic Freedom at Large Nf

Nf 3

QCD

16.5

QED-Like

g beta g beta anti-screening > screening anti-screening < screening

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

Emergence of Conformality in Perturbation

Nf 3

QCD

16.5

QED-Like

g beta g beta

N

g beta f *

Conformal Trans. (2nd.)

Miransky-Yamawaki ('97) c.f.: 2loop N = 8.05, Banks-Zaks ('82)

*

f

g*

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

Four-Loop Example

• 3
• 2
• 1

1 2 3 1 2 3 4 5 6 7 β g 4-loop beta-function, MS-bar Scheme Nf = 7.335 Nf = 8.0 1 2 3 4 5

• 4
• 2

2 4 α = − g2/4π log(− µ) 4-loop Running Coupling, MS-bar Scheme Nf = 7.335 Nf = 8.0 Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

IRFP Conformality

The emergence of IRFP Conformality due to the Non-Perturbative Gauge Interaction leads to a new class of a gauge theory different from both QCD and QED. (Lattice Reviews: Pallante, PoS LAT2009; Del Debbio, PoS LAT2010; Neil, PoS Lat2011). The IRFP (pre-)conformal dynamics plays an essential role in a technicolor model to implement a mass of standard model particles with avoiding too much FCNC (Review: Yamawaki (’96), Sannino (’06), Chivukula (’12)). The FRG method (Braun-Gies ’06-11) and the Gauge/Gravity model (Kiritsis et.al.(’08 - ’12), Kajantie et.al. (’09 - ’12), c.f. Panero (’09)) indicates that a cold conformal phase and a hot QGP phase is continuously connected at large Nf . In other words, the vanishing of the thermal chiral transition with increasing Nf indicates the onset of the conformal phase. Partly motivated by recent works of Shuryak (’12), the vanishing of the chiral dynamics is also elucidated by introducing the notion of a thermal critical coupling, whose approach to the IRFP coupling indicates the emergence of the conformal phase.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

IRFP Conformality

The emergence of IRFP Conformality due to the Non-Perturbative Gauge Interaction leads to a new class of a gauge theory different from both QCD and QED. (Lattice Reviews: Pallante, PoS LAT2009; Del Debbio, PoS LAT2010; Neil, PoS Lat2011). The IRFP (pre-)conformal dynamics plays an essential role in a technicolor model to implement a mass of standard model particles with avoiding too much FCNC (Review: Yamawaki (’96), Sannino (’06), Chivukula (’12)). The FRG method (Braun-Gies ’06-11) and the Gauge/Gravity model (Kiritsis et.al.(’08 - ’12), Kajantie et.al. (’09 - ’12), c.f. Panero (’09)) indicates that a cold conformal phase and a hot QGP phase is continuously connected at large Nf . In other words, the vanishing of the thermal chiral transition with increasing Nf indicates the onset of the conformal phase. Partly motivated by recent works of Shuryak (’12), the vanishing of the chiral dynamics is also elucidated by introducing the notion of a thermal critical coupling, whose approach to the IRFP coupling indicates the emergence of the conformal phase.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

IRFP Conformality

The emergence of IRFP Conformality due to the Non-Perturbative Gauge Interaction leads to a new class of a gauge theory different from both QCD and QED. (Lattice Reviews: Pallante, PoS LAT2009; Del Debbio, PoS LAT2010; Neil, PoS Lat2011). The IRFP (pre-)conformal dynamics plays an essential role in a technicolor model to implement a mass of standard model particles with avoiding too much FCNC (Review: Yamawaki (’96), Sannino (’06), Chivukula (’12)). The FRG method (Braun-Gies ’06-11) and the Gauge/Gravity model (Kiritsis et.al.(’08 - ’12), Kajantie et.al. (’09 - ’12), c.f. Panero (’09)) indicates that a cold conformal phase and a hot QGP phase is continuously connected at large Nf . In other words, the vanishing of the thermal chiral transition with increasing Nf indicates the onset of the conformal phase. Partly motivated by recent works of Shuryak (’12), the vanishing of the chiral dynamics is also elucidated by introducing the notion of a thermal critical coupling, whose approach to the IRFP coupling indicates the emergence of the conformal phase.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

IRFP Conformality

The emergence of IRFP Conformality due to the Non-Perturbative Gauge Interaction leads to a new class of a gauge theory different from both QCD and QED. (Lattice Reviews: Pallante, PoS LAT2009; Del Debbio, PoS LAT2010; Neil, PoS Lat2011). The IRFP (pre-)conformal dynamics plays an essential role in a technicolor model to implement a mass of standard model particles with avoiding too much FCNC (Review: Yamawaki (’96), Sannino (’06), Chivukula (’12)). The FRG method (Braun-Gies ’06-11) and the Gauge/Gravity model (Kiritsis et.al.(’08 - ’12), Kajantie et.al. (’09 - ’12), c.f. Panero (’09)) indicates that a cold conformal phase and a hot QGP phase is continuously connected at large Nf . In other words, the vanishing of the thermal chiral transition with increasing Nf indicates the onset of the conformal phase. Partly motivated by recent works of Shuryak (’12), the vanishing of the chiral dynamics is also elucidated by introducing the notion of a thermal critical coupling, whose approach to the IRFP coupling indicates the emergence of the conformal phase.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Emergence of IR-Conformality in Gauge Theory Motivation

Table of Contents

1

Introduction Emergence of IR-Conformality in Gauge Theory Motivation

2

Results Measurements and Lattice Outputs N∗

f from Vanishing Thermal step scalings

N∗

f from Thermal Critical Coupling g c T

N∗

f from Vanishing Critical Temperature Tc 3

Further Discussion: Two-Loop Asymptotics Scaling Analyses

4

Summary and Future Works

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Table of Contents

1

Introduction Emergence of IR-Conformality in Gauge Theory Motivation

2

Results Measurements and Lattice Outputs N∗

f from Vanishing Thermal step scalings

N∗

f from Thermal Critical Coupling g c T

N∗

f from Vanishing Critical Temperature Tc 3

Further Discussion: Two-Loop Asymptotics Scaling Analyses

4

Summary and Future Works

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Lattice Critical Coupling β c

L

0.25 0.5 0.75 1 1.25 1.5 1.75 4.6 4.8 5 5.2 5.4 5.6 βL fit for χσ χσ Rπ

In this example (Nf = 6, ma = 0.02, 243 × 8), we estimate the pseudo critical coupling to be β c

L = 5.20 ± 0.05 from the peak of chiral susceptibility χσ and

the drastic increase of the susceptibility ratio Rπ ≡ χσ/χπ.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Lattice Critical Coupling β c

L Table: Summary of β c

L = 10/(g c L )2. The entries with ∗ are the update for our

previous results (KM,Lombardo,Pallante 2011). The entries with † have been quoted from the previous studies on Nf = 8 (Deuzeman,Lombardo,Pallante, 2008). We have used ma = 0.02 for all finite Nf .

Nf \Nt 4 6 8 12 7.35 ± 0.05 7.97∗ ± 0.07 8.26 ± 0.06 − 4 5.65 ± 0.05 6.00∗ ± 0.05 6.15 ± 0.15 − 6 4.675∗ ± 0.05 5.025∗ ± 0.05 5.20∗ ± 0.05 5.55∗ ± 0.1 8 − 4.1125† ± 0.0125 4.275 ± 0.05 4.34† ± 0.04

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Thermal Step Scaling

The chiral transition temperature should be unique at fixed Nf : Tc = ˆ Nt a(g c

L )

˜−1 = ˆ N′

t a(g c L ′)

˜−1 , (1) The set {g c

L } satisfying this equation gives a non-perturbative running

coupling constructed by using the lattice measurements. Then, the vanishing (smaller) step-scaling ∆g c

L = g c L − g c L ′ ,

(2) at large Nf indicates a vanishing (slow) running coupling, or equivalently, (pre-)conformal dynamics.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Thermal step scalings in MY Diagram

5 6 7 8 9 10 11 12 13 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Nf gc=(10/βL

c)1/2

IRFP Candidate Nt=4 Nt=6 Nt=8 Nt=12

Figure: Tc =

ˆ Nt a(g c

L )

˜−1 = ˆ N′

t a(g c L ′)

˜−1 should holds at each Nf .

By using Nf = 6, 8 data, Nt = 6 and 12 lines get into the intersection at N∗

f ∼ 11.1 ± 1.6.

We also observe the stronger fermion screenings at larger Nf (c.f. Kogut et al. (’85)).

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Thermal step scalings in MY Diagram

5 6 7 8 9 10 11 12 13 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Nf gc=(10/βL

c)1/2

IRFP Candidate Nt=4 Nt=6 Nt=8 Nt=12

Figure: Tc =

ˆ Nt a(g c

L )

˜−1 = ˆ N′

t a(g c L ′)

˜−1 should holds at each Nf .

By using Nf = 6, 8 data, Nt = 6 and 12 lines get into the intersection at N∗

f ∼ 11.1 ± 1.6.

We also observe the stronger fermion screenings at larger Nf (c.f. Kogut et al. (’85)).

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Thermal step scalings in MY Diagram

5 6 7 8 9 10 11 12 13 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Nf gc=(10/βL

c)1/2

IRFP Candidate Nt=4 Nt=6 Nt=8 Nt=12

Figure: Tc =

ˆ Nt a(g c

L )

˜−1 = ˆ N′

t a(g c L ′)

˜−1 should holds at each Nf .

By using Nf = 6, 8 data, Nt = 6 and 12 lines get into the intersection at N∗

f ∼ 11.1 ± 1.6.

We also observe the stronger fermion screenings at larger Nf (c.f. Kogut et al. (’85)).

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Thermal Critical Coupling g c

T

We consider the renormalization flow from Tc to a−1(g c

L =

p 10/β c

L )

with the two-loop approximation: log h Tc a−1(gc) i = Z g c

T

g c

L

dg B2L(g) , Tc = ˆ Nt a(g c

L )

˜−1 . (3) The coupling g c

T gives a typical interaction strength at the scale µ = Tc.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Thermal Critical Coupling g c

T

We consider the renormalization flow from Tc to a−1(g c

L =

p 10/β c

L )

with the two-loop approximation: log h Tc a−1(gc) i = Z g c

T

g c

L

dg B2L(g) , Tc = ˆ Nt a(g c

L )

˜−1 . (3) The coupling g c

T gives a typical interaction strength at the scale µ = Tc.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

g c

T VS gc,SD and gIRFP,4l

2 4 6 8 10 12 14 1 1.5 2 2.5 3 Nf g

(Candidates)

gT

fit gT

gc,SD gIRFP,4l

IRFP

Thermal critical coupling g c

T meets the zero temperature critical couplings

estimated by the two-loop Schwinger Dyson equation (Appelquist et al, (’99)) or the IRFP coupling in the four-loop beta-function (Ryttov-Shrock (’12)) around N∗

f ∼ 12.5 ± 0.7.

Larger Nf gives more strongly interacting QGP! (c.f. Shuryak et al. (’12)).

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

g c

T VS gc,SD and gIRFP,4l

2 4 6 8 10 12 14 1 1.5 2 2.5 3 Nf g

(Candidates)

gT

fit gT

gc,SD gIRFP,4l

IRFP

Thermal critical coupling g c

T meets the zero temperature critical couplings

estimated by the two-loop Schwinger Dyson equation (Appelquist et al, (’99)) or the IRFP coupling in the four-loop beta-function (Ryttov-Shrock (’12)) around N∗

f ∼ 12.5 ± 0.7.

Larger Nf gives more strongly interacting QGP! (c.f. Shuryak et al. (’12)).

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

UV Reference Scale M

0.7 0.75 0.8 0.85 0.9 4 5 6 7 8 Tadpole Factor u0 βL Nf = 0 Nf = 4 Nf = 6 Nf = 8

Consider the two-loop renormalization flow which connects the scale Tc and some other scale M log h Tc M(g ref

L

) i = Z g c

T ∃g ref L

dg B2L(g) . (4) We extract the reference coupling g ref

L

from u0 ∼ 0.8 line with Nf independently, which results in a−1(g c

L ) M(g ref L

) ≫ Tc for all Nf .

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

UV Reference Scale M

0.7 0.75 0.8 0.85 0.9 4 5 6 7 8 Tadpole Factor u0 βL Nf = 0 Nf = 4 Nf = 6 Nf = 8

Consider the two-loop renormalization flow which connects the scale Tc and some other scale M log h Tc M(g ref

L

) i = Z g c

T ∃g ref L

dg B2L(g) . (4) We extract the reference coupling g ref

L

from u0 ∼ 0.8 line with Nf independently, which results in a−1(g c

L ) M(g ref L

) ≫ Tc for all Nf .

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Tc/M, with a UV scale M: Preliminary (c.f. Miura et.al. (’12))

0.1 0.2 0.3 0.4 0.5 4 5 6 7 8 9 10 11 12 Tc/M Nf u0 = 0.79 u0 = 0.80 u0 = 0.81 Nf*

Tc M(g ref

L

) = exp hZ g c

T

g ref

L

dg B2L(g) i ∼ K(N∗

f − Nf )−(2b2

0/b1)(N∗ f ) .(c.f. Braun-Gies,’11)

(5) N∗

f = 10.4 ± 1.2 for u0 = 0.79 − 0.81.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

Tc/M, with a UV scale M: Preliminary (c.f. Miura et.al. (’12))

0.1 0.2 0.3 0.4 0.5 4 5 6 7 8 9 10 11 12 Tc/M Nf u0 = 0.79 u0 = 0.80 u0 = 0.81 Nf*

Tc M(g ref

L

) = exp hZ g c

T

g ref

L

dg B2L(g) i ∼ K(N∗

f − Nf )−(2b2

0/b1)(N∗ f ) .(c.f. Braun-Gies,’11)

(5) N∗

f = 10.4 ± 1.2 for u0 = 0.79 − 0.81.

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works Measurements and Lattice Outputs N∗ f from Vanishing Thermal step scalings N∗ f from Thermal Critical Coupling g c T N∗ f from Vanishing Critical Temperature Tc

u0 dependences of N∗

f Preliminary (c.f. Miura et.al. (’12))

8 8.5 9 9.5 10 10.5 11 11.5 12 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 Nf* u0

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works

Table of Contents

1

Introduction Emergence of IR-Conformality in Gauge Theory Motivation

2

Results Measurements and Lattice Outputs N∗

f from Vanishing Thermal step scalings

N∗

f from Thermal Critical Coupling g c T

N∗

f from Vanishing Critical Temperature Tc 3

Further Discussion: Two-Loop Asymptotics Scaling Analyses

4

Summary and Future Works

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works

Two-Loop Asymptotic Scaling at Nf = 6

15 30 45 60 75 90 4 5 6 7 8 9 10 11 12 Tc/ΛE Nt

Tc/ΛE is almost Nt independent!! (c.f. Gupta (’06)).

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works

Two-Loop Asymptotic Scaling at Nf = 8

100 200 300 400 500 6 7 8 9 10 11 12 Nt Tc/ΛE Tc/ΛE

imp

It is difficult to make three data being consistent. ma = 0.02 effects? Far from continuum limit? Or something interesting?

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works

Table of Contents

1

Introduction Emergence of IR-Conformality in Gauge Theory Motivation

2

Results Measurements and Lattice Outputs N∗

f from Vanishing Thermal step scalings

N∗

f from Thermal Critical Coupling g c T

N∗

f from Vanishing Critical Temperature Tc 3

Further Discussion: Two-Loop Asymptotics Scaling Analyses

4

Summary and Future Works

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo

Introduction Results Further Discussion: Two-Loop Asymptotics Scaling Analyses Summary and Future Works

Summary

Thermodynamic Lattice Study for QCD-like Theory with IRFP Conformality (ma = 0.02)

N∗

f ∼

8 > < > : 11.1 ± 1.6 (the vanishing thermal scaling of β c

L ) ,

12.5 ± 0.7 (the approach of g c

T to gc,SD and gIRFP,4l) ,

10.4 ± 1.2 (the vanishing of Tc/M for u0 = 0.79 − 0.81) . (6) Future Works Thermodynamic and chiral limits, in particular at Nf = 8. To set a scale a−1 and complete T − Nf Phase Diagram: The potential measurement is on progress. Critical behavior near the IR-Fixed Pt. Gauge/Gravity Duality as a theoretical guide.

Thank you for your attention!

Kohtaroh MiuraA, M. LombardoA

• E. PallanteB , A. DeuzemanC , and T. SilvaB

Thermodynamic Lattice Study for Preconformal Dynamics in Strongly Flavo