Related papers: Eight dimensional physics and the Langlands progra…
We consider compactifications of the N=1, d=6, E_8 theory on tori to five, four, and three dimensions and learn about some properties of this theory. As a by-product we derive the SL(2,\IZ) duality of the N=2, d=4, SU(2) theory with N_f=4.…
We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further…
F-theory attempts to include all U-dualities manifestly. Unlike its T-dual manifest partner, which is based on string current algebra, F-theory is based on higher dimensional brane current algebra. Like the T-dual manifest theory, which has…
We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in…
The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an…
We derive general equations which determine the decomposition of the G^{+++} multiplet of brane charges into the sub-algebras that arise when the non-linearly realised G^{+++} theory is dimensionally reduced on a torus. We apply this to…
We demonstrate the emergence of the U-duality group in compactification of Matrix theory on a 4-torus. The discussion involves non-trivial effects in strongly coupled 4+1 dimensional gauge theory, and highlights some interesting phenomena…
We investigate domain-wall/quantum field theory correspondences in various dimensions. We give particular emphasis to the special case of the quantum mechanics of 0--branes.
We analyze six-dimensional supergravity theories coming from intersecting brane models on the toroidal orbifold T^4/Z_2. We use recently developed tools for mapping general 6D supergravity theories to F-theory to identify F-theory…
We argue that T-duality and F-theory appear automatically in the E_8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E_8 bundle. If we compactify on a two-torus, this data specifies an LLE_8…
A duality relationship between certain brane configurations in type IIA and type IIB string theory is explored by exploiting the geometrical origins of each theory in M-theory. The configurations are dual ways of realising the…
We study the interpretation of O7+ planes in F-theory, mainly in the context of the six-dimensional models. In particular, we study how to assign gauge algebras and matter content to seven-branes and their intersections, and the implication…
A proposed duality between type IIB superstring theory on R^9 X S^1 and a conjectured 11D fundamental theory (``M theory'') on R^9 X T^2 is investigated. Simple heuristic reasoning leads to a consistent picture relating the various p-branes…
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.
In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called `exotic branes'---low codimension objects with highly non-perturbative tensions, scaling as…
We construct dual Type I' string descriptions to five dimensional supersymmetric fixed points with $E_{N_f+1}$ global symmetry. The background is obtained as the near horizon geometry of the D4-D8 brane system in massive Type IIA…
Recent developments involving strongly coupled superstrings are discussed from a phenomenological point of view. In particular, strongly coupled $E_8\times E'_8$ is described as an appropriate long-wavelength limit of M-theory, and some…
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the…
We give a preliminary discussion of how the addition of extra coordinates in M-theory, which together with the original ones parametrise a U-fold, can serve as a tool for formulating brane dynamics with manifest U-duality. The redundant…
In this paper we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the non-perturbative dynamics of the three-dimensional field theory via a T-duality at finite radius and the…