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Chiral holography

Atul Sharma, David Skinner

TL;DR

This work constructs a top-down holographic dual for the self-dual sector of $ ext{N}=4$ sYM via a twistor-string setup, identifying a B-model on a backreacted 14-real-dimensional bulk with $N$ units of flux as the gravity side. It develops a nonstandard holographic dictionary, relating twistorial $6d$ currents and determinant operators to BCOV bulk modes and giant graviton branes, respectively, and shows how determinant correlators reduce to a ρ-matrix model whose saddles map to open-string vacua on D5' giants. The analysis unifies twistorial open- and closed-string dynamics, clarifies locality issues in the twistorial setting, and demonstrates that half-BPS correlators can be captured by bulk giant brane configurations, providing a tractable laboratory for holography at zero coupling. The results open avenues to connect to AdS$_5 imes S^5$ physics, extend to supersymmetric determinant sectors, and probe amplitude/Wilson loop dualities in a chiral holographic framework with potential implications for higher-spin and ABJM-like theories.

Abstract

Using twistor string theory, we engineer a gravitational holographic dual of the self-dual sector of $\mathcal{N}=4$ super Yang-Mills theory. This provides a top-down example of holography at zero 't Hooft coupling. Our holographic dictionary operates at the level of D-branes wrapping twistor lines and generalizes the D-instanton prescription used to compute scattering amplitudes. As an application, we study the correlators of determinant operators that act as generating functions of half-BPS operators in the self-dual theory. We show that these correlators are dual to configurations of giant gravitons in the bulk.

Chiral holography

TL;DR

This work constructs a top-down holographic dual for the self-dual sector of sYM via a twistor-string setup, identifying a B-model on a backreacted 14-real-dimensional bulk with units of flux as the gravity side. It develops a nonstandard holographic dictionary, relating twistorial currents and determinant operators to BCOV bulk modes and giant graviton branes, respectively, and shows how determinant correlators reduce to a ρ-matrix model whose saddles map to open-string vacua on D5' giants. The analysis unifies twistorial open- and closed-string dynamics, clarifies locality issues in the twistorial setting, and demonstrates that half-BPS correlators can be captured by bulk giant brane configurations, providing a tractable laboratory for holography at zero coupling. The results open avenues to connect to AdS physics, extend to supersymmetric determinant sectors, and probe amplitude/Wilson loop dualities in a chiral holographic framework with potential implications for higher-spin and ABJM-like theories.

Abstract

Using twistor string theory, we engineer a gravitational holographic dual of the self-dual sector of super Yang-Mills theory. This provides a top-down example of holography at zero 't Hooft coupling. Our holographic dictionary operates at the level of D-branes wrapping twistor lines and generalizes the D-instanton prescription used to compute scattering amplitudes. As an application, we study the correlators of determinant operators that act as generating functions of half-BPS operators in the self-dual theory. We show that these correlators are dual to configurations of giant gravitons in the bulk.

Paper Structure

This paper contains 49 sections, 277 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Self-duality and holography.
  3. A fresh look at twistor strings.
  4. A non-standard holographic dictionary.
  5. Determinants and giant gravitons.
  6. $\mathcal{N}=4$ self-dual Yang-Mills
  7. A chiral free limit
  8. Open twistor string theory
  9. Twistor geometry.
  10. Twistor strings.
  11. Reduction to spacetime.
  12. The gravitational dual
  13. Closed twistor string theory
  14. Brane backreaction
  15. Boundary structure.
  16. ...and 34 more sections

Figures (1)

  • Figure 1: The D$5'$ giant gravitons start life as coincident branes. They are sent to their desired locations in the target space via Higgsing their worldvolume theory. We have displayed the 5-$5'$ and $5'$-5 strings $\chi_{ir},\widetilde{\chi}_i^r$ stretching from the $N$ D5 branes to the D$5'$ giants. Post backreaction, they get replaced by the fermion bilinears $\rho_{ij}=\chi_{ir}\widetilde{\chi}_j^r$ introduced during the Hubbard-Stratonovich transform. The $\rho_{ij}$ will be identified with nontrivial states of strings stretching across non-coincident giants, signaling recombination of the 5-$5'$ and $5'$-5 strings into $5'$-$5'$ strings in the presence of flux.