By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry.
We show that in an asymptotically free gauge theory, the contribution of heavy quarks to deep inelastic structure functions can be computed in terms of the contributions of light quarks. In the standard model with four quark multiplets and an SU(3) gauge group, we estimate that for 10 GeV2 < Q 2 < 40 GeV2 the charmed quark contribution to structure functions will be several percent for x < 0.2 and tenths of a percent for x < 0.2. Our main theoretical tool is an expansion, analogous to the usual operator product expansion, of an operator constructed from heavy quark fields as a sum of light quark and gluon operators with c-number coefficients. This expansion is valied order by order in perturbation theory.
A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean
The Gopakumar-Vafa (GV) formula expresses certain couplings that arise in Type IIA compactification to four dimensions on a Calabi-Yau manifold in terms of a counting of BPS states in M-theory. The couplings in question have applications to topological strings and supersymmetric black holes. In this paper, we reconsider the GV formula, taking a close look at the Schwinger-like computation that was suggested in the original GV work. The goal is to understand the background that must be used in this computation, the role played by the extended supersymmetry of this background, and how the computation gives a holomorphic result though superficially depending only on particle masses. We also examine in a similar way the Ooguri-Vafa (OV) formula, which is an extension of the GV formula to include D4-branes.
In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of ``surface operators,'' which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on curves. We describe the relevant surface operators in N=4 super Yang-Mills theory, and the parameters they depend on, and analyze how S-duality acts on these parameters. Then, after compactifying on a Riemann surface, we show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification. The construction involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification, and an action of the affine braid group on A-branes or B-branes on this space.
Two dimensional quantum Yang-Mills theory is reexamined using a non-abelian version of the Duistermaat-Heckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressions for intersection pairings on moduli spaces of flat connections on a two dimensional surface. The latter expressions agree, for gauge group SU (2), with formulas obtained recently by several methods.
We generalize the super period matrix of a super Riemann surface to the case that Ramond punctures are present. For a super Riemann surface of genus g with 2 r Ramond punctures, we define, modulo certain choices that generalize those in the classical theory (and assuming a certain generic condition is satisfied), a g | r × g | r period matrix that is symmetric in the Z 2 -graded sense. As an application, we analyze the genus 2 vacuum amplitude in string theory compactifications to four dimensions that are supersymmetric at tree level. We find an explanation for a result that has been found in orbifold examples in explicit computations by D’Hoker and Phong: with their integration procedure, the genus 2 vacuum amplitude always vanishes “pointwise” after summing over spin structures, and hence is given entirely by a boundary contribution.
'The index of the dirac operator in loop space' published in 'Elliptic Curves and Modular Forms in Algebraic Topology'
We investigate the statistical mechanics of a gas of fractional statistics particles in 2+1 dimensions. In the case of statistics very close to Fermi statistics (statistical parameter θ=π(1−1/n), for large n), the effect of the statistics is a weak attraction. Building upon earlier RPA calculation of Fetter, Hanna, and Laughlin for the case n=2, we argue that for large n perturbation theory is reliable and exhibits superfluidity (or superconductivity after coupling to electromagnetism). We attempt to describe the order parameter for this superconducting phase in terms of “spontaneous breaking of commutativity of translations” as opposed to the usual pairing order parameters. The vortices of the superconducting anyon gas are charged, and superconducting order parameters of the usual type vanish. We investigate the characteristic P and T violating phenomenology.
The mystery of the cosmological constant is probably the most pressing obstacle to significantly improving the models of elementary particle physics derived from string theory. The problem arises because in the standard framework of low energy physics, there appears to be no natural explanation for vanishing or extreme smallness of the vacuum energy, while on the other hand it is very difficult to modify this framework in a sensible way. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted in terms of a vacuum state with unbroken supersymmetry.
No abstract is provided for this article.
The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be avoided.
No abstract is provided for this article.
Geometric Langlands duality relates a representation of a simple Lie group G v to the cohomology of a certain moduli space associated with the dual group G. In this correspondence, a principal SL 2 subgroup of G v makes an unexpected appearance. This can be explained using gauge theory, as this paper will show, with the help of the equations of Nahm and Bogomolny.
We present a gauge-theoretic interpretation of the “analytic” version of the geometric Langlands program, in which Hitchin Hamiltonians and Hec
Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and have the expected infrared behavior. The main technical tool is to make the whole analysis, including especially those arguments that involve integration by parts, on supermoduli space, rather than after descending to ordinary moduli space.
Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a ``dual'' equation in which the gauge group is the dual of the maximal torus of $SU(2)$. The new viewpoint suggests many new results about the Donaldson invariants.
Recently, background-independent open-string field theory has been formally defined in the space of all two-dimensional world-sheet theories. In this paper, to make the construction more concrete, I compute the action for an off-shell tachyon field of a certain simple type. From the computation it emerges that, although the string field action does not coincide with the world-sheet (matter) partition function in general, these functions do coincide on shell. This can be demonstrated in general, as long as matter and ghosts are decoupled.
