802 publications from this institution
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the concept of ``supersymmetry'' of particle interactions. There are hints from the successes of supersymmetric unified theories of particle interactions that supersymmetry is relevant to elementary particles at energies close to current accelerator energies; if this is so, it will be confirmed experimentally and supersymmetry is then also likely to be important in cosmology, in connection with dark matter, baryogenesis, and/or inflation. Magnetic monopoles play an important role in the structure of string theory, and thus should certainly exist, if string theory is correct, though they may have been diluted by inflation to an unobservable level. The monopole mass in many attractive models is near the Planck mass, but, if unification of elementary particle forces with gravity occurs near TeV energies through large or warped extra dimensions, as in some recent models, then monopoles should be below 100 TeV and in an astrophysical context would be ultrarelativistic. In such models, supersymmetry would definitely be expected at TeV energies.
On the world-volume of an M-theory five-brane propagates a two-form with self-dual field strength. As this field is non-Lagrangian, there is no obvious framework for determining its partition function. An analogous problem exists in Type IIB superstring theory for the self-dual five-form. The resolution of these problems and definition of the partition function is explained. A more complete analysis of perturbative anomaly cancellation for M-theory five-branes is also presented, uncovering some surprising details.
The connection of recently constructed lower dimensional heterotic strings with conventional toroidal compactification is clarified.
We re-examine quantization via branes with the goal of understanding its relation to geometric quantization. If a symplectic manifold $M$ can be quantized in geometric quantization using a polarization ${\mathcal P}$, and in brane quantization using a complexification $Y$, then the two quantizations agree if ${\mathcal P}$ can be analytically continued to a holomorphic polarization of $Y$. We also show, roughly, that the automorphism group of $M$ that is realized as a group of symmetries in brane quantization of $M$ is the group of symplectomorphisms of $M$ that can be analytically continued to holomorphic symplectomorphisms of $Y$. We describe from the point of view of brane quantization several examples in which geometric quantization with different polarizations gives equivalent results.
No abstract is provided for this article.
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \S7 of certain facts that may be relevant to constructing the ``mirror map'' between mirror moduli spaces.
Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking a complex structure on $C$ and using Hitchin's equations. We sketch the essential statements both for the ``unramified'' case that $C$ is a compact oriented two-manifold without boundary, and the ``ramified'' case that one allows punctures. We also give a few indications of why a more precise description requires a starting point in four-dimensional gauge theory.
Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.
We prove that for genus g � 5, the moduli space of super Rie- mann surfaces is not projected (and in particular is not split): it cannot be holomorphically projected to its underlying reduced manifold. Physically, this means that certain approaches to superstring perturbation theory that are very powerful in low orders have no close analog in higher orders. Mathemat- ically, it means that the moduli space of super Riemann surfaces cannot be constructed in an elementary way starting with the moduli space of ordinary Riemann surfaces. It has a life of its own.
A bstract Generalizing previous results for $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 0 and $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1, we analyze $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 JT supergravity on asymptotically AdS 2 spaces with arbitrary topology and show that this theory of gravity is dual, in a holographic sense, to a certain random matrix ensemble in which supermultiplets of different R -charge are statistically independent and each is described by its own $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 random matrix ensemble. We also analyze the case with a time-reversal symmetry, either commuting or anticommuting with the R -charge. In order to compare supergravity to random matrix theory, we develop an $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 analog of the recursion relations for Weil-Petersson volumes originally discovered by Mirzakhani in the bosonic case.
In his later years, Einstein sought a unified theory that would extend general relativity and provide an alternative to quantum theory. There is now talk of a ‘theory of everything’ (although Einstein himself never used the phrase). Fifty years after his death, how close are we to such a theory?
These lectures notes provide a general introduction to grand unified theories and their supersymmetric generalizations.
This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics that was held at the IAS as well as the New Zealand Mathematical Research Institute summer school held in Nelson in January, 2020.
Surface operators in gauge theory are analogous to Wilson and 't Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve.In a previous paper, we constructed a certain class of half-BPS surface operators in N = 4 super Yang-Mills theory, and determined how they transform under S-duality.Those surface operators depend on a relatively large number of freely adjustable parameters.In the present paper, we consider the opposite case of half-BPS surface operators that are "rigid" in the sense that they do not depend on any parameters at all.We present some simple constructions of rigid half-BPS surface operators and attempt to determine how they transform under duality.This attempt is only partially successful, suggesting that our constructions are not the whole story.The partial match suggests interesting connections with quantization.We discuss some possible refinements and some string theory constructions which might lead to a more complete picture.
Must general relativity finally bow to quantum mechanics? Calculations that describe black-hole properties using collections of superstrings have gone some way towards resolving one of the most vexing puzzles in physics.
We reformulate the Ω-deformation of four-dimensional gauge theory in a way that is valid away from fixed points of the associated group action. We use this reformulation together with the theory of coisotropic A-branes to explain recent results linking the Ω-deformation to integrable Hamiltonian systems in one direction and Liouville theory of two-dimensional conformal field theory in another direction.
These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)
In N = 1 super Yang-Mills theory in three spacetime dimensions, with a simple gauge group G and a Chern-Simons interaction of level k, the supersymmetric index Tr (-1) F can be computed by making a relation to a pure Chern-Simons theory or microscopically by an explicit Born-Oppenheimer calculation on a two-torus.The result shows that supersymmetry is unbroken if |k| ≥ h/2 (with h the dual Coxeter number of G) and suggests that dynamical supersymmetry breaking occurs for |k| < h/2.The theories with large |k| are massive gauge theories whose universality class is not fully described by the standard criteria.
