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Semiclassics, branes, and extremality

Adolfo Holguin

Abstract

We revisit the problem of computing extremal and non-extremal three point functions of semiclassical probes with single trace operators and point out certain inconsistencies in previous approaches in the literature. We clarify the roles of wavefunctions and averaging over moduli, concluding that holographic computations may be performed with or without averaging. By carefully implementing the extrapolate dictionary for extremal correlators we explain the origin of the apparent mismatch between supergravity and CFT for extremal correlators involving giant gravitons in type IIB supergravity. We propose an ansatz for the wavefunctions of half-BPS giants which reproduces large $N$ limit of certain extremal two and three point functions in $\mathcal{N}=4$ SYM.

Semiclassics, branes, and extremality

Abstract

We revisit the problem of computing extremal and non-extremal three point functions of semiclassical probes with single trace operators and point out certain inconsistencies in previous approaches in the literature. We clarify the roles of wavefunctions and averaging over moduli, concluding that holographic computations may be performed with or without averaging. By carefully implementing the extrapolate dictionary for extremal correlators we explain the origin of the apparent mismatch between supergravity and CFT for extremal correlators involving giant gravitons in type IIB supergravity. We propose an ansatz for the wavefunctions of half-BPS giants which reproduces large limit of certain extremal two and three point functions in SYM.
Paper Structure (19 sections, 98 equations, 4 figures)

This paper contains 19 sections, 98 equations, 4 figures.

Table of Contents

  1. Introduction
  2. HHL correlators and semiclassics
  3. Giant Graviton Correlators
  4. To average or not to average: counting moduli
  5. Why computing without averaging gives the right answer
  6. Why averaging and not averaging both fail
  7. Semiclassics and D-branes
  8. Coherent State Path Integrals
  9. Toy Effective Action
  10. Giant effective action revisited
  11. Non-extremal Correlators
  12. Extremal Correlators
  13. Canonical Quantization and Brane Wavefunctions
  14. Quantizing LLM
  15. Brane Wavefunctions
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Sketch of the Lorentzian computation of the one point function. The red dot indicated the location of the bulk vertex which is integrated along the worldvolume of the probe. The initial and final state are inserted in the Euclidean segments of the geometry. The Euclidean caps prepate the initial and final states for the Lorentzian time evolution.
  • Figure 2: The Euclidean calculation implicitly performed in Yang:2021kot. The Euclidean solution shares the $t=0$ slice with the Lorentzian one. Note the integration over the bulk vertex is completely within the Euclidean region. This is interpreted there as the integration over the moduli "$\tau_0$".
  • Figure 3: Sketch of the extremal three point function. The insertion of the light operator is taken to be on the Euclidean cap corresponding to the initial state. This inserts an additional half-BPS operator on the south pole of $S^4$ multiplied by a phase factor arising from the boundary propagator.
  • Figure 4: An example of a test surface $\Sigma$ over which we measure the five form flux. The surface extends along the $y$ direction of the geometry and an $S^3$ is fibered over it creating a non-trivial five-cycle.