Giant Gravitons and non-conformal vacua in twisted holography

Twisted holography relates the two-dimensional chiral algebra subsector of $\mathcal{N}=4$ SYM to the B-model topological string theory on the deformed conifold $SL(2,\mathbb{C})$. We review the relevant aspects of the duality and its two generalizations: the correspondence between determinant operators and "Giant Graviton" branes and the extension to non-conformal vacua of the chiral algebra.Comment: 12 pages, contribution to proceedings of String Math 202

Giant gravitons in twisted holography

We study correlation functions of determinant-like operators in the "chiral algebra subsector" of four-dimensional ${\cal N}=4$ gauge theory with $U(N)$ gauge group. We map the the large-$N$ saddles of the correlation functions to specific semiclassical D-branes in the holographic dual BCOV theory. We present a detailed match of several gauge-theory and BCOV calculations.Comment: 39 pages, 2 figures, added acknowledgements and minor edit

Twisted holography without conformal symmetry

We discuss the notion of translation-invariant vacua for 2d chiral algebras and relate it to the notion of the associated variety. The two-dimensional chiral algebra associated to four-dimensional ${\cal N}=4$ $U(N)$ SYM has a conjectural holographic dual involving the B-model topological string theory. We study the effect of non-zero vacuum expectation values on the chiral algebra correlation functions and derive a holographic dual Calabi-Yau geometry. We test our proposal by a large $N$ analysis of correlation functions of determinant operators, whose saddles can be matched with semi-classical configurations of "Giant Graviton" D-branes in the bulkComment: 17 pages, no figure

Following Black Hole States

We study $\mathcal{N}=4$ SYM at non-integer number of colours. By varying $N$ we can continuously follow states all the way from $N=\infty$ where integrability reigns to finite $N$ where quantum gravity effects dominate. As an application we consider classically $1/16$ BPS states. Quantum mechanically, these states are generically non-supersymmetric but some special states -- at special values of $N$ -- become super-symmetric at the quantum level as well. They are the so-called quantum black hole states studied recently using cohomology. We write down the form of the lightest BH state at $N=2$ -- and follow it in $N$, both at weak coupling and -- more speculatively -- at strong coupling as well. At weak coupling this state has protected dimension $\Delta=19/2$ at $N=2$ and becomes a triple trace made out of Konishi and two light BPS operators at infinite $N$ with $\Delta=19/2+12\lambda+\dots$. At strong coupling we suspect it becomes a quadruple trace with dimension $\Delta \simeq 19/2+\text{integer}$.Comment: 7+8 pages, 20 footnote

Semi-Chiral Operators in 4d N=1{\cal N}=1 Gauge Theories

We discuss the properties of quarter-BPS local operators in four dimensional ${\cal N}=1$ supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to algebraic operations which endow the twisted theory with an infinite symmetry algebra. We classify all single-trace quarter-BPS operators in the planar approximation for $SU(N)$ gauge theory and propose a holographic dual description for the twisted theory. We classify perturbative quarter-BPS operators in $SU(2)$ and $SU(3)$ gauge theories with sufficiently small quantum numbers and discuss possible non-perturbative corrections to the answer. We set up analogous calculations for some theories with matter.Comment: 55+20 pages, 61 footnotes, comments welcom

Strings2024 Conference

Twisted holography relates the 2d chiral algebra subsector of N=4 SYM to the B-model topological string theory on the complex manifold SL(2,C). In this talk, I will present the correspondence between determinant operators and “Giant Graviton” branes. In particular, the large N saddles of determinant correlation functions can be matched with semiclassical D-brane configurations and determinant modifications with brane excitations. I will also discuss twisted holography duals of 4d holomorphic theories and their analogous correspondence

Giant gravitons in twisted holography

Abstract We study correlation functions of determinant-like operators in the “chiral algebra subsector” of four-dimensional N $$\mathcal{N}$$ = 4 gauge theory with U(N) gauge group. We map the large N saddles of the correlation functions to specific semiclassical D-branes in the holographic dual BCOV theory. We present a detailed match of several gauge-theory and BCOV calculations

Feynman diagrams in four-dimensional holomorphic theories and the Operatope

Abstract We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories