Revisiting soliton contributions to perturbative processes Andy - - PowerPoint PPT Presentation

Revisiting soliton contributions to perturbative processes

Andy Royston

Texas A&M University

Strings, Princeton, June 26, 2014

Based on 1403.5017 and 1404.0016 with C. Papageorgakis

Gong Show, Round 16 Even the “Fight of the Century” went only 15 rounds

Q & A

Q: Do solitons run in loops? A: Yes, in the following sense:

2 Im

• k

k k

f

f df

2

• Q:
• Can we compute their contribution to perturbative processes?
• Is this contribution “exponentially suppressed”? (in what quantity?)1

A:

• Yes, under certain assumptions.
• Usually, but not necessarily. (in the ratio Rc/RS.)

1Drukier and Nussinov (1982)..., Demidov and Levkov (2011), Banks (2012)

How do we compute?

Use analyticity and crossing symmetry:

t k

S S

p1 p2 k

S S

p1' p2 cross

Apair-prod(k2) = Ascat(k2)

• p′

1=−p1

compute Ascat perturbatively in soliton sector:

δ(k + p′

1 − p2)Ascat(k2) = S(p2)|T{e−i

• dtHI }|k, S(p′

1)

Exhibiting suppression

• consider class of scalar models φ(x) = φS
• x−x0

RS ; . . .

Exhibiting suppression

• consider class of scalar models φ(x) = φS
• x−x0

RS ; . . .

• find Apair−prod(k2) vanishes faster than any power in the ratio

Rc/RS for k2 above† threshold (2MS)2

†need to understand threshold effects better

Exhibiting suppression

• consider class of scalar models φ(x) = φS
• x−x0

RS ; . . .

• find Apair−prod(k2) “exponentially suppressed” in the ratio

Rc/RS for k2 above† threshold (2MS)2 Apair−prod(k2) e−2RS/Rc . . .

†need to understand threshold effects better

Exhibiting suppression

• consider class of scalar models φ(x) = φS
• x−x0

RS ; . . .

• find Apair−prod(k2) “exponentially suppressed” in the ratio

Rc/RS for k2 above† threshold (2MS)2 Apair−prod(k2) e−2RS/Rc . . .

• provided RS bounded away from zero (as a function on the moduli

space of soliton solutions)

†need to understand threshold effects better

Possible lessons for 5D MSYM

• first take off the EFT glasses and suppose that 5D MSYM is a

microscopic theory

• ⇒ integrate over all loop momenta (i.e. ΛUV → ∞)
• but then, for k2 > (2MS)2, will produce S-S pairs
• RS = ρ → 0 so argument for exponential suppression breaks down,

suggesting soliton contributions may compete

• unfortunately approx. scheme also breaks down...need new methods

Possible lessons for 5D MSYM

• first take off the EFT glasses and suppose that 5D MSYM is a

microscopic theory

• ⇒ integrate over all loop momenta (i.e. ΛUV → ∞)
• but then, for k2 > (2MS)2, will produce S-S pairs
• RS = ρ → 0 so argument for exponential suppression breaks down,

suggesting soliton contributions may compete

• unfortunately approx. scheme also breaks down...need new methods

Thank you!

example with internal modulus3

L = 1 2 (∂µφ∂µφ + ∂µχ∂µχ) − 1 2 (W 2 φ + W 2 χ) W = χ − 1 3 χ3 − χφ2 − β 3 φ3 ⇒ φ(χ) = βχ + b

• β2 + 4 −
• (χ
• β2 + 4 + βb)2 + 4(b2 − 1)

2 , χ(x) =

• b2 − 1

β2 + 4    2 tanh(x − x0) + 2b

• b2 − 1(
• β2 + 4 − β)

−

• b2 − 1(
• β2 + 4 − β)

2 tanh(x − x0) + 2b − βb

• b2 − 1

  

10 8 6 4 2 2 4 xx0 1.0 0.5 0.5 1.0 Χ 10 8 6 4 2 2 4 xx0 0.2 0.4 0.6 0.8 Φ 3BNRT (1997); Brito and de Souza Dutra (2014)