Related papers: Toric Duality as Seiberg Duality and Brane Diamond…
We consider the analogue of Seiberg duality for two-dimensional $N=(2,2)$ gauge theory with orthogonal gauge groups and with fundamental chiral multiplets proposed by Hori. Following Hori, when we consider $O(N)$ gauge group as the…
We study the recently proposed crystal model for three dimensional superconformal field theories arising from M2-branes probing toric Calabi-Yau four-fold singularities. We explain the algorithms mapping a toric Calabi-Yau to a crystal and…
In this paper we discuss two aspects of duality transformations on the Neveu-Schwarz (NS) 5-brane solutions in type II and heterotic string theories. First we demonstrate that the non-extremal NS 5-brane background is U-dual to its CGHS…
We study the dynamics of a single M2-brane probing toric Calabi-Yau four-fold singularity in the context of the recently proposed M-theory crystal model of AdS4/CFT3 dual pairs. We obtain an effective abelian gauge theory in which the…
We report on a broad new class of N=1 gauge theory dualities which relate the worldvolume gauge theories of D3 branes probing different orientifolds of the same Calabi-Yau singularity. In this paper, we focus on the simplest example of…
We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin…
By analyzing $F$-theory on $K3$ near the orbifold limit of $K3$ we establish the equivalence between $F$-theory on $K3$ and an orientifold of type IIB on $T^2$, which in turn, is related by a T-duality transformation to type I theory on…
The self-duality of Dirichlet $3$-brane action under the $SL(2,R)$ duality transformation of type IIB superstring theory is shown in the Hamiltonian form of the path integral for the partition function by performing the direct integration…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
We investigate different toric phases of 2+1 dimensional quiver gauge theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane tiling for each toric phase is presented. We apply the 'forward algorithm' to obtain the toric…
Recently, a D-brane construction in type IIA string theory was shown to yield the electric/magnetic duality of four dimensional N=1 supersymmetric U(N_c) gauge theories with N_f flavours of quark. We present here an extension of that…
This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic…
We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact…
We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is…
The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on…
We study (0,2) supersymmetric two-dimensional theories obtained by compactifying four-dimensional N=1 supersymmetric theories on a two-torus, with a magnetic field for a global U(1) symmetry, and present evidence that Seiberg duality in…
The toric code, when deformed in a way that preserves the self-duality $\mathbb{Z}_2$ symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the…
We develop the non-perturbative reduced phase space quantization of causal diamonds in (2+1)-dimensional gravity with a nonpositive cosmological constant. In this Part I we focus on the classical reduction process, and the description of…
Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories. The brane tiling data consists of a bipartite…
This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…