Related papers: Simple-Sum Giant Graviton Expansions for Orbifolds…
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…
The superconformal index of $\mathcal N=4$ super-Yang Mills theory with $U(N)$ gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms…
We study asymptotics of the $d=4$, $\mathcal{N}=1$ superconformal index for toric quiver gauge theories. Using graph-theoretic and algebraic factorization techniques, we obtain a cycle expansion for the large-$N$ index in terms of the…
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…
We investigate a simple-sum giant graviton expansion of the superconformal indices of ${\cal N}=2$ superconformal field theories realized on D3-branes probing $7$-brane backgrounds with constant axio-dilation field. The expansion is of…
M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories coupled to gravity. We propose a new construction of such $\mathrm{Spin}(7)$-manifolds, based…
We investigate the mathematical and physical content of the giant graviton expansion of three-dimensional $\mathcal{N}=4$ superconformal field theories in a simplifying limit. We uncover an interesting relation between the coefficients in…
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…
We consider four dimensional ${\cal N}=1$ supersymmetric gauge theories obtained via orientifolds of Type IIB on Abelian C^3/G orbifolds. We construct all such theories that have well defined world-sheet expansion. The number of such…
We compute the prepotential for gauge theories descending from ${\cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive…
We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface $\Sigma_g$, with an arbitrary partial topological twist for the global $U(1)$ symmetries.…
We use a generalised Kummer construction to realise all but one known weight four newforms with complex multiplication and rational Fourier coefficients in smooth Calabi-Yau threefolds defined over the rational numbers. The Calabi-Yau…
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of…
We consider $\mathcal{N} = 2$ superconformal gauge theories in four dimensions. We explain how these quiver gauge theories arise as low-energy worldvolume theories of D3-branes on orientifolds. Then, we examine their associated chiral…
We extend the formulation of gauged supergravity in five dimensions, as obtained by compactification of $M$~theory on a deformed Calabi-Yau manifold, to include non-universal matter hypermultiplets. Even in the presence of this gauging,…
For a toric Calabi-Yau (CY) orbifold $\mathcal{X}$ whose underlying toric variety is semi-projective, we construct and study a non-toric Lagrangian torus fibration on $\mathcal{X}$, which we call the Gross fibration. We apply the…
We present an explicit supersymmetric deformation of supergravity backgrounds describing D3-branes on Calabi-Yau cones. From the geometrical point of view, it corresponds to blowing up a 4-cycle in the Calabi-Yau and can be done…
We consider topological closed string theories on Calabi-Yau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition…
Generalized complex geometry is an example of a powerful formalism to attempt the construction of a language adequate to string theory. With the remarkable property of unifying symplectic and complex manifolds as special cases of a broader…
We compute the index for orbifold quiver gauge theories. We compare it with the results obtained from the type IIB supergravity (superstring) on AdS_5 \times S^5/\Gamma.