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Holographic thermal correlators from supersymmetric instantons

by Matthew Dodelson, Alba Grassi, Cristoforo Iossa, Daniel Panea Lichtig, Alexander Zhiboedov

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Submission summary

Authors (as registered SciPost users): Matthew Dodelson
Submission information
Preprint Link: scipost_202301_00043v1  (pdf)
Date accepted: 2023-03-23
Date submitted: 2023-01-31 15:26
Submitted by: Dodelson, Matthew
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement.

Published as SciPost Phys. 14, 116 (2023)

Author comments upon resubmission

We would like to thank the referees for their careful reading of the manuscript and the valuable comments and suggestions.
Below we have included our response to their specific comments/suggestions.

List of changes

Report 1:

1. We expect the analytic properties of G_R to be related to the particular form of the singularities of the NS functions (see [78-79]).
However it is fair to say that we currently we do not have a detailed understanding of this aspect. We hope to report on this in the future.

2. The large spin quasinormal modes have exponentially suppressed imaginary part, so they are the leading contribution to the Green's function at late times (to leading order in 1/c_T). We added a comment on this point in the first paragraph of Section V.C.

3. Appendix C contains definitions of some special functions. The purpose of this appendix is mainly to explain what conventions we are using. For this reason, we would prefer to keep these technical aspects in the appendix. Instead, we have moved some of Appendix F to the main text (see the discussion around (32)). We hope this addresses the reviewer's suggestion.

Report 2:

1. From the point of view of the SUSY gauge theory there is no discrimination between ingoing and outgoing waves. The connection coefficients for both problems can be expressed using the NS functions, and the result for the outgoing problem is a slight modification of (26). We have added a comment to this effect in Footnote 6.

2. At present this relation appears to be a mathematical coincidence. Perhaps a more physical explanation will be found in the future.

3. We agree with this point, and have moved some of the discussion in Appendix F to the main text (see the discussion around (32)).

Submission & Refereeing History

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Resubmission scipost_202301_00043v1 on 31 January 2023

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