相关论文: Finite $N$ indices and the giant graviton expansio…
We consider a class of matrix integrals over the unitary group $U(N)$ with an infinite set of couplings characterized by a series $f(q)=\sum_{n \ge 1} a_n q^n$, with $a_n \in \mathbb{Z}$. Such integrals arise in physics as the partition…
We propose and test a novel conjectural relation satisfied by the superconformal index of maximally supersymmetric $U(N)$ gauge theory in four dimensions. Analogous relations appear to be also valid for the superconformal indices of a large…
The superconformal index of half-BPS states in ${\cal N}=4$ supersymmetric Yang-Mills with gauge group $U(N)$ admits an expansion in terms of giant gravitons, ${\cal I}_N(q)={\cal I}_\infty(q) \sum\limits_{m=0}^\infty q^{mN}\hat{\mathcal…
Work by Gaiotto and Lee, and by Imamura and collaborators suggests that the superconformal index of $U(N)$ gauge theory should be expressible as a convergent series whose terms are indices of associated $U(k)$ gauge theories realized as the…
The superconformal index of $\frac12$-BPS states of $N=4$ U(N) super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by…
The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using…
We study the giant graviton integrated correlator in SU$(N)$ $\mathcal{N}=4$ super Yang-Mills at finite complexified coupling $\tau$. Despite the formidable complexity arising from the heavy nature of the operators considered, the large-$N$…
Certain correlation functions are computed exactly in the zero coupling limit of N=4 super Yang-Mills theory with gauge group SU(N). A set of linearly independent operators that are in one-to-one correspondence with the half-BPS…
Recently, S. Murthy has proposed a convergent expansion of free partition functions and superconformal indices of finite-$N$ purely adjoint gauge theories based on a Fredholm determinant expansion. This expansion has been dubbed the giant…
We discuss giant graviton expansions for the Schur index of ${\cal N}=4$ $U(N)$ SYM with the insertion of Wilson lines of the fundamental and the anti-fundamental representations. We first propose a double-sum giant graviton expansion and…
We propose a prescription to calculate the superconformal index of the ${\cal N}=4$ $U(N)$ supersymmetric Yang-Mills theory with finite $N$ on the AdS side. The finite $N$ corrections are included as contributions of D3-branes wrapped…
There is now strong evidence that the superconformal index of holographic gauge theories admits a giant graviton expansion capturing the worldvolume dynamics of spherical D3-branes moving in internal space. While the giant graviton indices…
The superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with gauge group $\mathrm{U}(N)$ has provided powerful insights into the entropy of supersymmetric black holes in AdS$_5\times S^5$, including some sub-leading…
We use Monte Carlo methods to directly evaluate D-dimensional SU(N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for…
We study giant graviton expansions of the superconformal index of 4d orbifold/orientifold theories. In general, a giant graviton expansion is given as a multiple sum over wrapping numbers. It has been known that the expansion can be reduced…
The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory with a general classical gauge group…
We apply numerical and analytic techniques to the study of Yang-Mills integrals with orthogonal, symplectic and exceptional gauge symmetries. The main focus is on the supersymmetric integrals, which correspond essentially to the bulk part…
We identify the operators in ${\cal N}=4$ super Yang-Mills theory that correspond to ${1\over 8}$-BPS giant gravitons in AdS$_5\times$S$^5$. Our evidence for the identification comes from (1) counting these operators and showing agreement…
We generalize the Gervais-Neveu gauge to four-dimensional N=1 superspace. The model describes an N=2 super Yang-Mills theory. All chiral superfields (N=2 matter and ghost multiplets) exactly cancel to all loops. The remaining hermitian…
We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of…