802 publications from this institution
These notes are based on lectures at the PSSCMP/PiTP summer school that was held at Princeton University and the Institute for Advanced Study in July, 2015. They are devoted largely to topological phases of matter that can be understood in terms of free fermions and band theory. They also contain an introduction to the fractional quantum Hall effect from the point of view of effective field theory.
To understand in detail duality between heterotic string and F theory compactifications, it is important to understand the construction of holomorphic G bu
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.
No abstract is provided for this article.
Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from cla
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.
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.
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 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 quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi–Yau structure on a six-dimensional manifold,
Some recent developments in string field theory are discussed and a perspective on the subject is given.
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.
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...
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.)
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 .
