arXiv subjects

Edward Witten

Publications and source records attributed to Edward Witten.

At least 145 records · Page 8Linked to original sources

arXiv2003

Chern-Simons Gauge Theory As A String Theory

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.

hep-th↗

arXiv2003

A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory

We make contact between the infinite-dimensional non-local symmetry of the typeIIB superstring on AdS5xS5 worldsheet theory and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the Hamiltonian of a spin chain, and show that it commutes with the g*2 N = 0 limit of the non-abelian charges.

hep-th↗

arXiv2003

SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry

On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group $SL(2,{\bf Z})$. The generator $S$ of $SL(2,{\bf Z})$ acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator $T$ acts by shifting the Chern-Simons coupling of the background field. This $SL(2,{\bf Z})$ action in three dimensions is related by the AdS/CFT correspondence to $SL(2,{\bf Z})$ duality of low energy U(1) gauge fields in four dimensions.

hep-th↗

arXiv2003

Chiral Ring Of Sp(N) And SO(N) Supersymmetric Gauge Theory In Four Dimensions

The chiral ring of classical supersymmetric Yang-Mills theory with gauge group $Sp(N)$ or SO(N) is computed, extending previous work (of Cachazo, Douglas, Seiberg, and the author) for SU(N). The result is that, as has been conjectured, the ring is generated by the usual glueball superfield $S\sim \Tr W_αW^α$, with the relation $S^h=0$, $h$ being the dual Coxeter number. Though this proposition has important implications for the behavior of the quantum theory, the statement and (for the most part) the proofs amount to assertions about Lie groups with no direct reference to gauge theory.

hep-th↗

arXiv2003

A Note On The Chern-Simons And Kodama Wavefunctions

Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction. It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting to understand what it describes. We show that in expanding around this state, positive helicity gauge bosons have positive energy and negative helicity ones have negative energy. Some of the negative energy states would have negative norm. We also show that the Chern-Simons state is the supersymmetric partner of the naive fermion vacuum in which one does not fill the fermi sea. Finally, we give a sort of explanation of ``why'' this state exists. Similar properties can be expected for the analogous Kodama wavefunction of gravity.

gr-qc↗

arXiv2003

Proton Decay in Intersecting D-brane Models

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 coresponding result in four-dimensional GUT's. 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 $10^{36}$ years.

hep-th↗

arXiv2003

A Derivation of K-Theory from M-Theory

We show how some aspects of the K-theory classification of RR fluxes follow from a careful analysis of the phase of the M-theory action. This is a shortened and simplified companion paper to ``E8 Gauge Theory, and a Derivation of K-Theory from M-Theory.''

hep-th↗

arXiv2003

Residues and World-Sheet Instantons

We reconsider the question of which Calabi-Yau compactifications of the heterotic string are stable under world-sheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0,2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. Here, we show that this cancellation follows directly from a residue theorem, whose proof relies only upon the right-moving world-sheet supersymmetries and suitable compactness properties of the (0,2) linear sigma model. Our residue theorem also extends to a new class of "half-linear" sigma models. Using these half-linear models, we show that heterotic compactifications on the quintic hypersurface in CP^4 for which the gauge bundle pulls back from a bundle on CP^4 are stable. Finally, we apply similar ideas to compute the superpotential contributions from families of membrane instantons in M-theory compactifications on manifolds of G_2 holonomy.

hep-th↗

arXiv2003

Chiral Rings and Phases of Supersymmetric Gauge Theories

We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a meromorphic one-form on a Riemann surface. The equations of motion are equivalent to a condition on the integrality of periods of this form. The solution indicates that all semiclassical phases with the same number of U(1) factors are continuously connected.

hep-th↗

arXiv2003

Phases of N=1 Supersymmetric Gauge Theories and Matrices

N=1 supersymmetric U(N) gauge theory with adjoint matter $Φ$ and a polynomial superpotential $\Tr W(Φ)$ has been much studied recently. The classical theory has several vacua labeled by integers $(N_1,N_2,...,N_k)$, with the classical unbroken gauge group $\prod_i U(N_i)$. Quantum mechanically, each classical vacuum leads to $\prod_i N_i$ different vacua. As the parameters of $W(Φ)$ are varied, these vacua change in a continuous (and holomorphic) fashion. We find that vacua associated with $(N_1,N_2,...,N_k)$ can be continuously transformed to vacua with $(\tilde N_1,\tilde N_2,...,\tilde N_k)$, thus leading to a new kind of duality. Traditional order parameters, like the Wilson loop and 't Hooft loop, sometimes distinguish different phases. We also find phases that are not distinguished by conventional order parameters. The whole picture of the phase diagram is reminiscent of the phase diagram of $M$-theory.

hep-th↗

arXiv2002

Comments On String Theory

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.

hep-th↗

arXiv2002

Chiral Rings and Anomalies in Supersymmetric Gauge Theory

Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of $\N=1$ super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.

hep-th↗

arXiv2002

Singularities in string theory

String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework for geometry that reduces to ordinary differential geometry when the curvature is asymptotically small. In the 1990's, many interesting results were obtained about the behavior of string theory in spacetimes that develop singularities. In many cases, the physics at the singularity is governed by an effective Lagrangian constructed using an interesting bit of classical geometry such as the association of A-D-E groups with certain hypersurface singularities or the ADHM construction of instantons. In other examples, the physics at the singularity cannot be described in classical terms but involves a non-Gaussian conformal field theory.

hep-th↗

arXiv2002

A Note on Fluxes and Superpotentials in M-theory Compactifications on Manifolds of G_2 Holonomy

We consider the breaking of N=1 supersymmetry by non-zero G-flux when M-theory is compactified on a smooth manifold X of G_2 holonomy. Gukov has proposed a superpotential W to describe this breaking in the low-energy effective theory. We check this proposal by comparing the bosonic potential implied by W with the corresponding potential deduced from the eleven-dimensional supergravity action. One interesting aspect of this check is that, though W depends explicitly only on G-flux supported on X, W also describes the breaking of supersymmetry by G-flux transverse to X.

hep-th↗

arXiv2002

Quest For Unification

The GUT-based approach to physics has been attractive since it was first put forward close to thirty years ago; it has been enriched by new ideas, notably supersymmetry and strings; and there are real hints that it is on the right track, notably from measurements of the weak mixing angle and neutrino masses. In this article (based on my Heinrich Hertz lecture at SUSY 2002 at DESY, June, 2002), some of the arguments for grand unification will be reviewed.

hep-ph↗

arXiv2002

A Gravity Dual of the Chiral Anomaly

We study effects associated with the chiral anomaly for a cascading $SU(N+M)\times SU(N)$ gauge theory using gauge/gravity duality. In the gravity dual the anomaly is a classical feature of the supergravity solution, and the breaking of the U(1) R-symmetry down to ${\bf Z}_{2M}$ proceeds via the Higgs mechanism.

hep-th↗

arXiv2002

BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field

The D0-D6 system, which is not supersymmetric in the absence of a Neveu-Schwarz B-field, becomes supersymmetric if a suitable constant B-field is turned on. On one side of the supersymmetric locus, this system has a BPS bound state, and on the other side it does not. After compactification on T^6, this gives a simple example in which the number of 1/8 BPS states jumps as the moduli of the compactification are changed. The D0-D8 system in a B-field has two different supersymmetric loci, only one of which is continuously connected to the familiar supersymmetric D0-D8 system without a B-field. In a certain range, the D0-D8 system also has a BPS bound state. In the limit in which the B-field goes to infinity, supersymmetric D0-D6 and D0-D8 systems and their bound states can be studied using noncommutative Yang-Mills theory.

hep-th↗

arXiv2002

Deconstruction, G_2 Holonomy, and Doublet-Triplet Splitting

We describe a mechanism for using discrete symmetries to solve the doublet-triplet splitting problem of four-dimensional supersymmetric GUT's. We present two versions of the mechanism, one via ``deconstruction,'' and one in terms of M-theory compactification to four dimensions on a manifold of G_2 holonomy.

hep-ph↗