Publications

Vector Bundles and F Theory

To understand in detail duality between heterotic string and F theory compactifications, it is important to understand the construction of holomorphic G bu

Fivebranes and Knots

We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern-Simons gauge theory on the boundary of the D3-brane worldvolume; on the other hand, it can be studied by standard techniques of $S$-duality and $T$-duality. Combining the two approaches leads to a new and manifestly invariant description of the Jones polynomial of knots, and its generalizations, and to a manifestly invariant description of Khovanov homology, in terms of certain elliptic partial differential equations in four and five dimensions.

Isadore M. Singer (1924–2021) In Memoriam Part 1: Scientific Works

No abstract is provided for this article.

Петлевые амплитуды, аномалиии феноменология

No abstract is provided for this article.

Perturbative expansion of Chern-Simons theory with non-compact gauge group

Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads

Quantum gravity partition functions in three dimensions

We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from cla

Supersymmetry and Morse theory

It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian.Some of the implications of modern ideas in mathematics for supersymmetric theories are discussed.

謎めいた"M理論"--双対性,時空,量子力学

No abstract is provided for this article.

On orbifolds with discrete torsion

We consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain “tringy regions” that from a classical point of view are singularities that are to be neither resolved nor blown up. Some of these models also give particularly simple and clear examples of mirror symmetry.

Topological gravity in two dimensions

We derive two-dimensional topological gravity, which previously has been discussed in a BRST framework, by gauge fixing of an underlying gauge invariant system. The underlying lagrangian is zero.

The Timelike Tube Theorem in Curved Spacetime

The timelike tube theorem asserts that in quantum field theory without gravity, the algebra of observables in an open set U is the same as the corresponding algebra of observables in its ``timelike envelope'' E(U), which is an open set that is in general larger. The theorem was originally proved in the 1960's by Borchers and Araki for quantum fields in Minkowski space. Here we sketch the proof of a version of the theorem for quantum fields in a general real analytic spacetime. Details have appeared elsewhere.

The Hitchin Functionals and the Topological B-Model at One Loop

The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi–Yau structure on a six-dimensional manifold,

Some Remarks about String Field Theory

Some recent developments in string field theory are discussed and a perspective on the subject is given.

Analytic Continuation Of Chern-Simons Theory

The title of this article refers to analytic continuation of three-dimensional Chern-Simons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the volume conjecture, or analytic continuation of three-dimensional quantum gravity (to the extent that it can be described by gauge theory) from Lorentzian to Euclidean signature. Such analytic continuation can be carried out by rotating the integration cycle of the Feynman path integral. Morse theory or Picard-Lefschetz theory gives a natural framework for describing the appropriate integration cycles. An important part of the analysis involves flow equations that turn out to have a surprising four-dimensional symmetry. After developing a general framework, we describe some specific examples (involving the trefoil and figure-eight knots in S^3). We also find that the of possible integration cycles for Chern-Simons theory can be interpreted as the physical Hilbert space of a twisted version of N=4 super Yang-Mills theory in four dimensions.

Kaluza-Klein Theory and the Positive Energy Theorem

These lecture notes deal with two topics that I believe are closely related. The first topic is the Kaluza-Klein theory — an old approach to unification of gauge fields with general relativity which is now more interesting than ever. The second topic is the...

Erratum to: “CFT's from Calabi–Yau four-folds”

Geometric Langlands from six dimensions

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 understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)

Short distance analysis of weak interactions

We systematically formulate the short distance analysis of weak interactions, and show that in an asymptotically free theory one can calculate the dependence of any weak amplitude on the W boson and heavy quark masses. Our main purpose is to settle some conceptual questions, but we also derive some new quantitative results. For example, we show that in the SU(3) gauge theory with four quark triplets, the two W boson contribution to KL → μμ will differ from the free quark theory estimate by a factor 25(1 − (α(M W /α(m p′) 1 25 )(α(M W )/α(m p′ )) 24 25 . We also show that the amplitudes for K+ → π +e+e− will differ from the free quark theory estimate by a factor of 1.66(α(M W )/α(m p′)) 2 9 − 1.88(α(M W )/α(m p′) −4 9 .