D-Brane Systems in Twisted Holography and SO/Sp Chiral Algebras

TL;DR

This work develops a Twisted Holography dictionary between boundary chiral algebras and bulk D-brane systems, recasting dual branes as derived coherent sheaves on $SL_2(\mathbb{C})$ and extending the construction from $U(N)$ to $SO/Sp$ gauge groups. It analyzes correlation functions of determinant and baryon operators, obtains ADHM-like complexes encoding the dual branes, and demonstrates $\mathbb{Z}_2$ identifications consistent with Kodaira–Spencer orientifolds and Type I topological string theories. The approach provides a covariant, symmetry-respecting BRST framework and a unified spectral-curve/complex description of branes, offering evidence for the conjectured bulk duals and paving the way for instanton-like deformations in chiral algebras across gauge groups. The results have implications for understanding holographic duals of chiral algebras and for connecting Twisted Holography to orientifolded bulk theories.

Abstract

We study correlation functions of baryon and determinant operators for the chiral algebras obtained from the twist of N = 4 SYM with U(N) gauge group. In the context of Twisted Holography, we conjecture that a dual description should involve a D1-D5 brane system, and we construct from the correlators a candidate dual brane in the form of a derived coherent sheaf in SL(2,C). Extending this analysis, we compute similar baryon/determinant correlators of chiral algebras in symmetric and antisymmetric representations of SO and Sp gauge groups and construct the candidate dual branes. These branes exhibit Z_2 identifications consistent with conjectures relating SO/Sp chiral algebras to Kodaira-Spencer theory on SL(2,C)/Z_2 and the Type I topological string on SL(2,C).

Figures (1)

• Figure 1: Schematic representation of the brane as a complex curve in $SL_2(\mathbb{C})$. The complex curve asymptotes to the boundary determinant insertions.