802 publications from this institution
Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time interpretations. For instance, three-dimensional Chern-Simons gauge theory can arise as a string theory. The world-sheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the space-time Chern-Simons theory. A certain holomorphic analog of Chern-Simons theory can also arise as a string theory.
No abstract is provided for this article.
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.
We study, using the dual AdS description, the vacua of field theories where some of the gauge symmetry is broken by expectation values of scalar fields. In such vacua, operators built out of the scalar fields acquire expectation values, and we show how to calculate them from the behavior of perturbations to the AdS background near the boundary. Specific examples include the N = 4 SYM theory, and theories on D3-branes placed on orbifolds and conifolds. We also clarify some subtleties of the AdS/CFT correspondence that arise in this analysis. In particular, we explain how scalar fields in AdS space of sufficiently negative mass-squared can be associated with CFT operators of two possible dimensions. All dimensions are bounded from below by (d−2)/2; this is the unitarity bound for scalar operators in d-dimensional field theory. We further argue that the generating functional for correlators in the theory with one choice of operator dimension is a Legendre transform of the generating functional in the theory with the other choice.
The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi–Yau structure on a six-dimensional manifold,
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...
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 .
The possible astrophysical role of superstrings is discussed. Type II superstrings (if somehow phenomenologically viable) might be seen as gravitational lenses. The superstrings of the new O(32) and E8×E8 string theories are boundaries of axion domain walls. These theories are also likely to generate more “conventional” string-like objects-stable vortex lines and flux tubes.
We compute static properties of baryons in an SU(2) × SU(2) chiral theory (the Skyrme model) whose solitons can be interpreted as the baryons of QCD. Our results are generally within about 30% of experimental values. We also derive some relations that hold generally in soliton models of baryons, and therefore, serve as tests of the 1 N expansion.
In 1900, in the course of trying to fit to experimental data, Planck wrote down his celebrated formula for black body radiation. It does not usually happen in physics that an experimental curve is directly related to the fundamentals of a theory; normally they are related by a more or less intricate chain of calculations. But black body radiation was a lucky exception to this rule. In fitting to experimental curves, Planck wrote down a formula that directly led, as we all know, to the concept of the quantum.
No abstract is provided for this article.
The standard boundary state of a topological insulator in 3+1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological order. Our models are weakly coupled and all the dynamics is explicit. We rederive some known boundary states of topological insulators and construct new ones. Consistency with the standard spin/charge relation of condensed matter physics places a nontrivial constraint on models.
No abstract is provided for this article.
We analyze proton decay via dimension-six operators in certain GUT-like models derived from Type IIA orientifolds with D6-branes. The amplitude is parametrically enhanced by a factor of α GUT −1/3 relative to the corresponding result in four-dimensional GUTs. Nonetheless, even assuming a plausible enhancement from the threshold corrections, we find little overall enhancement of the proton decay rate from dimension-six operators, so that the predicted lifetime from this mechanism remains close to 1036 years.
N = 2 supersymmetric gauge theories in four dimensions are studied by formulating them as the quantum field theories derived from configurations of fourbranes, fivebranes, and sixbranes in Type IIA superstrings, and then reinterpreting those configurations in M-theory. This approach leads to explicit solutions for the Coulomb branch of a large family of four-dimensional N = 2 field theories with zero or negative beta function.
Our basic ideas about physics went through several upheavals early this century. Quantum mechanics taught us that the classical notions of the position and velocity of a particle were only approximations of the truth. With general relativity, spacetime became a dynamical variable, curving in response to mass and energy. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new source of “fuzziness” may enter physics, and spacetime itself may be reinterpreted as an approximate, derived concept. (See figure 1.) In this article I survey some of these developments.
We investigate the differential geometry of the moduli space of instantons on S^3 x S^1. Extending previous results, we show
that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry, supporting speculations that this sigma-model may be dual to Type IIB superstring theory on AdS_3 x S^3 x S^3 x S^1. The sigma-model is parametrized by three integers -- the rank of the gauge
group, the instanton number, and a ``level'' (the integer coefficient of a topologically nontrivial B-field, analogous to a WZW level). 
These integers are expected to correspond to two five-brane charges and
a one-brane charge. The sigma-model is weakly coupled when the level, conjecturally corresponding to one of the five-brane changes, becomes very large, keeping the
other parameters fixed. The central charges of the large N=4 algebra agree, at least semiclassically, with expectations from the duality.
An attempt is made to construct a realistic model of particle physics based on eleven-dimensional supergravity with seven dimensions compactified. It is possible to obtain an SU(3) × SU(2) × U(1) gauge group, but the proper fermion quantum numbers are difficult to achieve.
