ON ABJM BDS EXPONENTIATION Matias Leoni Universidad de Buenos - - PowerPoint PPT Presentation

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ON ABJM BDS EXPONENTIATION Matias Leoni Universidad de Buenos - - PowerPoint PPT Presentation

Dec 05, 2023 114 likes •416 views

ON ABJM BDS EXPONENTIATION Matias Leoni Universidad de Buenos Aires & CONICET In collaboration with Marco S. Bianchi arXiv:1403.3398 N=4 SYM Exponentiation Consider color ordered MHV 4p amplitude in We define the ratio

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SLIDE 1

ON ABJM BDS EXPONENTIATION

Matias Leoni Universidad de Buenos Aires & CONICET

In collaboration with Marco S. Bianchi arXiv:1403.3398

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SLIDE 2

N=4 SYM Exponentiation

Consider color ordered MHV 4p amplitude in We define the ratio s.t. 1 loop 2 loop 3 loop BDS Ansatz

Bern, Dixon, Smirnov hep-th/0505205

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SLIDE 3

N=4 SYM Exponentiation

Consider color ordered MHV 4p amplitude in We define the ratio s.t. 1 loop 2 loop 3 loop BDS Ansatz

Bern, Dixon, Smirnov hep-th/0505205

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SLIDE 4

N=4 SYM Exponentiation

Consider color ordered MHV 4p amplitude in We define the ratio s.t.

1 loop 2 loop 3 loop

BDS Ansatz

Bern, Dixon, Smirnov hep-th/0505205

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SLIDE 5

N=4 SYM Exponentiation

Consider color ordered MHV 4p amplitude in We define the ratio s.t.

1 loop 2 loop

3 loop BDS Ansatz

Bern, Dixon, Smirnov hep-th/0505205

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SLIDE 6

N=4 SYM Exponentiation

Consider color ordered MHV 4p amplitude in We define the ratio s.t.

1 loop 2 loop 3 loop

BDS Ansatz

Bern, Dixon, Smirnov hep-th/0505205

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SLIDE 7

N=4 SYM Exponentiation

Consider color ordered MHV 4p amplitude in We define the ratio s.t.

1 loop 2 loop 3 loop

BDS Ansatz

Bern, Dixon, Smirnov hep-th/0505205

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SLIDE 8

ABJM Theory

  • 3D Superconformal field Theory
  • N=6 SUSY, 24 supercharges
  • Dual to IIA Strings on
  • Two CS fields
  • Matter in the bifundamental:

Aharony, Bergman, Jafferis, Maldacena arXiv:0806.1218

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SLIDE 9

ABJM Theory

  • 3D Superconformal field Theory
  • N=6 SUSY, 24 supercharges
  • Dual to IIA Strings on
  • Two CS fields
  • Matter in the bifundamental:

Aharony, Bergman, Jafferis, Maldacena arXiv:0806.1218

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SLIDE 10

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

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SLIDE 11

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 12

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 13

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 14

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 15

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 16

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 17

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 18

ABJM scattering amplitudes

On shell: 4 p. Superamplitude:

1 loop: 2 loops:

Unitarity Cuts Integrand of 3 loop result

Bianchi, ML, Mauri, Penati, Santambrogio arXiv:1107.3139; Chen, Huang arXiv:1107.2710

Bargheer, Loebbert, Meneghelli, arXiv:1003.6120

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SLIDE 19

Results

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 20

Results

Main Result: Recall: Then

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 21

Results

Main Result: Recall: Then

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 22

Results

Main Result: Recall: Then

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 23

Results

Main Result: Recall: Then

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 24

Results

Main Result: Recall: Then

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 25

Results

Main Result: Recall: Then

  • M. S. Bianchi, ML, arXiv:1403.3398
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SLIDE 26

Conclusions

  • Evidence for exponentiation - DCI??
  • Not clear from strong coupling
  • Compared to N=4:

➔ Odd loops: disappear from exponent ➔ Even loops similar to N=4 SYM

 Would need 4 loops to see if recurrence is satisfied

with 2 loop result

Drummond, Henn, Korchemsky, Sokatchev, arXiv:0712.1223

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SLIDE 27

Conclusions

  • Evidence for exponentiation - DCI??
  • Not clear from strong coupling
  • Compared to N=4:

➔ Odd loops: disappear from exponent ➔ Even loops similar to N=4 SYM

 Would need 4 loops to see if recurrence is satisfied

with 2 loop result

Drummond, Henn, Korchemsky, Sokatchev, arXiv:0712.1223 Adam, Dekel, Oz, arXiv:1008.0649 Bakhmatov, Colgain, Yavartanoo, arXiv:1109.1052

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SLIDE 28

Conclusions

  • Evidence for exponentiation - DCI??
  • Not clear from strong coupling
  • Compared to N=4:

➔ Odd loops: disappear from exponent ➔ Even loops similar to N=4 SYM

 Would need 4 loops to see if recurrence is satisfied

with 2 loop result

Drummond, Henn, Korchemsky, Sokatchev, arXiv:0712.1223 Adam, Dekel, Oz, arXiv:1008.0649 Bakhmatov, Colgain, Yavartanoo, arXiv:1109.1052

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SLIDE 29

Conclusions

  • Evidence for exponentiation - DCI??
  • Not clear from strong coupling
  • Compared to N=4:

➔ Odd loops: disappear from exponent ➔ Even loops similar to N=4 SYM

 Need 4 loops to verify if recurrence is satisfied with

2 loop result

Drummond, Henn, Korchemsky, Sokatchev, arXiv:0712.1223 Adam, Dekel, Oz, arXiv:1008.0649 Bakhmatov, Colgain, Yavartanoo, arXiv:1109.1052