Related papers: Eight dimensional physics and the Langlands progra…
We review quantitative tests on the duality between the heterotic string on T^2 and F-theory on K3. On the heterotic side, certain threshold corrections to the effective action can be exactly computed at one-loop order, and the issue is to…
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…
A recent attempt to extend the geometric Langlands duality to affine Kac-Moody groups, has led Braverman and Finkelberg [arXiv:0711.2083] to conjecture a mathematical relation between the intersection cohomology of the moduli space of…
One of the dualities in string theory, the F-theory/heterotic string duality in eight dimensions, predicts an interesting correspondence between two seemingly disparate geometrical objects. On one side of the duality there are elliptically…
We propose a duality in the relative Langlands program. This duality pairs a Hamiltonian space for a group $G$ with a Hamiltonian space under its dual group $\check{G}$, and recovers at a numerical level the relationship between a period on…
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories…
Using the general properties that have emerged from E theory we sketch the generic features of the dynamics of branes in seven and eight dimensions. The dynamical equations are a set of duality equations involving the coordinates of the…
We initiate the program of bottom-up derivation of string theory dualities using Swampland principles. In particular, we clarify the relation between Swampland arguments and all the string theory dualities in $d\geq9$ dimensional…
A variant of the topological twist, involving SL(2,Z) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kaehler space with holomorphically…
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
We study the D-brane solutions to type IIB superstring in ten dimensions and find interpretation in terms of compactification of a twelve dimensional three-brane of (a specific) F-theory on a torus $T^2$. In this frame-work, there also…
We study D-brane actions in non-relativistic string theory. We consider single D-brane and analyse its properties under T-duality. We also derive an action for N D8-branes and also for lower dimensional D-branes through T-duality…
The purpose of this paper is to investigate the possibility of a physical 12-dimensional F-theory. We study the question of geometric interaction terms in the F-theory Lagrangians. We also introduce a new supergravity multiplet in dimension…
This presentation is intended to give a flavour of the physics to be studied and discovered by exploiting the interface between string theory, M-theory and field theory provided by the dynamics of extended objects called `branes', and their…
Applying string dualities to F-theory, we obtain various $[p,q]$-branes whose constituents are standard branes of codimension two and exotic branes. We construct junctions of the exotic five-branes and their Hanany-Witten transitions…
We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.
This talk is divided into two parts. The first part reviews some of the duality relationships between superstring theories. These relationships are interpreted as providing evidence for the existence of a unique underlying fundamental…
Recent developments in superstring theory have led to major advances in understanding. After reviewing where things stood earlier, we sketch the impact of recently identified dualities and D-branes, as well as a hidden eleventh dimension.
Langlands duality is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic…