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802 publications from this institution

Self-duality, Ramond-Ramond fields, and K-theory

No abstract is provided for this article.

Gregory W. Moore, Edward Witten 2000Article

New Perspectives in the Quest for Unification

Edward Witten 1998Article

Branes and Supergroups

Extending previous work that involved D3-branes ending on a fivebrane with $${\theta_{\mathrm{YM}}\neq 0}$$ , we consider a similar two-sided problem. This

Victor Mikhaylov, Edward Witten 2015Article

An Introduction To The Web-Based Formalism

This paper summarizes our rather lengthy paper, "Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions," and is meant to be an informal, yet detailed, introduction and summary of that larger work.

Davide Gaiotto, Gregory W. Moore, Edward Witten 2015Preprint

Limits on massless particles

We show that in all theories with a Lorentz-covariant energy-momentum tensor, such as all known renormalizable quantum field theories, composite as well as elementary massless particles with j > 1 are forbidden. Also, in all theories with a Lorentz-covariant conserved current, such as renormalizable theories with a symmetry that commutes with all local symmetries, there cannot exist composite or elementary particles with nonvanishing values of the corresponding charge and j > 1/2.

Steven Weinberg, Edward Witten 1980Article

String theory and geometry

No abstract is provided for this article.

Edward Witten, Felix E. Browder 1988Book

Anti De Sitter Space And Holography

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

Edward Witten 1998Preprint

Anomalies, dualities, and topology of D = 6 N = 1 superstring vacua

We consider various aspects of compactifications of the Type 1/heterotic Spin(32)/Z 2 theory on K3. One family of such compactifications includes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of the heterotic E 8 × E 8 theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory recently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E 8 × E 8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z 2 and E 8 × E 8 models can be demonstrated by T-duality, and permit a better understanding of nonperturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/Z 2 and E 8 × E 8 models, the strong/weak coupling duality of the (12,12) E 8 × E 8 model is mapped to T-duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism.

Micha Berkooz, Robert G. Leigh, Joseph Polchinski et al. 1996Article

GRAND UNIFICATION IN FOUR-DIMENSIONS OR TEN-DIMENSIONS

No abstract is provided for this article.

Edward Witten 1985Article

References

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Michael Green, John H. Schwarz, Edward Witten 2012Chapter in a book

Galaxy Formation With Massive Neutrinos

No abstract is provided for this article.

C. Pryor, M. Davis, M. Lecar et al. 1980Article

Mirror symmetry as a gauge symmetry

It is shown that in string theory mirror duality is a gauge symmetry (a Weyl transformation) in the moduli space of N = 2 backgrounds on group manifolds, and we conjecture on the possible generalization to other backgrounds, such as Calabi-Yau manifolds.

Amit Giveon, Edward Witten 1994Article

Conservation laws in some two-dimensional models

Certain classical conservation laws in the chiral O (N) × O (N) and SU (N) × SU (N) models in two dimensions are shown to survive quantization. This indicates that the S matrices of these models must factorize. At least in one case that is checked explicitly, an analogous conservation law in the CP N model does not appear to survive quantization.

Yadin Y. Goldschmidt, Edward Witten 1980Article

Shelter Island, II

No abstract is provided for this article.

R. Jackiw, Nocola N. Khuri, Steven Weinberg et al. 1985Article

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of spin- 1 2 or -3 2 or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.

Luis Álvarez-Gaumé, Edward Witten 1984Article

The Feynman $i \epsilon$ in String Theory

The Feynman $i\varepsilon$ is an important ingredient in defining perturbative scattering amplitudes in field theory. Here we describe its analog in string theory. Roughly one takes the string worldsheet to have Lorentz signature when a string is going on-shell although it has Euclidean signature generically.

Edward Witten 2013Preprint

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q 2 dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F 2 will, at large Q 2, exceed the free quark result by a factor 1.751, while for x = 0.5, F 2 is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.

Edward Witten 1977Article

Gravity and the Crossed Product

Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III$_1$ in the operator algebra of ${\mathcal N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\infty$. The Type II$_\infty$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_\infty$ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.

Edward Witten 2021Preprint

NOTES ON ‘STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: I & II’

This chapter discusses Edwards' early work trying to devise a convenient description of topological constraint in order to study the statistical physics of cross-linked polymers, which is related to modern descriptions of topological knots.

Edward Witten 2004Chapter in a book

Small instantons in string theory

A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra SU(2) gauge symmetry appears that is supported in the core of the instanton. Thus in particular the quantum heterotic string has vacua with higher rank than is possible in conformal field theory. When k instantons collapse at the same point, the enhanced gauge symmetry is Sp(k). These results, which can be tested by comparison to Dirichlet five-branes of Type I superstrings and to the ADHM construction of instantons, give the first example for the heterotic string of a non-perturbative phenomenon that cannot be turned off by making the coupling smaller. They have applications to several interesting puzzles about string duality.

Edward Witten 1996Article

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Publications

Self-duality, Ramond-Ramond fields, and K-theory

New Perspectives in the Quest for Unification

Branes and Supergroups

An Introduction To The Web-Based Formalism

Limits on massless particles

String theory and geometry

Anti De Sitter Space And Holography

Anomalies, dualities, and topology of D = 6 N = 1 superstring vacua

GRAND UNIFICATION IN FOUR-DIMENSIONS OR TEN-DIMENSIONS

References

Galaxy Formation With Massive Neutrinos

Mirror symmetry as a gauge symmetry

Conservation laws in some two-dimensional models

Shelter Island, II

Gravitational anomalies

The Feynman $i \epsilon$ in String Theory

Anomalous cross section for photon-photon scattering in gauge theories

Gravity and the Crossed Product

NOTES ON ‘STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: I &amp; II’

Small instantons in string theory

NOTES ON ‘STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: I & II’