arXiv subjects

N. Seiberg

Publications and source records attributed to N. Seiberg.

At least 19 recordsLinked to original sources

arXiv2006

A Note on (Meta)stable Brane Configurations in MQCD

We examine the M-theory version of SQCD which is known as MQCD. In the IIA limit, this theory appears to have a supersymmetry-breaking brane configuration which corresponds to the meta-stable state of N=1 SU(Nc) SQCD. However, the behavior at infinity of this non-supersymmetric brane construction differs from that of the supersymmetric ground state of MQCD. We interpret this to mean that it is not a meta-stable state in MQCD, but rather a state in another theory. This provides a concrete example of the fact that, while MQCD accurately describes the supersymmetric features of SCQD, it fails to reproduce its non-supersymmetric features (such as meta-stable states) not only quantitatively but also qualitatively.

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arXiv2003

A New Hat For The c=1 Matrix Model

We consider two dimensional supergravity coupled to $\hat c=1$ matter. This system can also be interpreted as noncritical type 0 string theory in a two dimensional target space. After reviewing and extending the traditional descriptions of this class of theories, we provide a matrix model description. The 0B theory is similar to the realization of two dimensional bosonic string theory via matrix quantum mechanics in an inverted harmonic oscillator potential; the difference is that we expand around a non-perturbatively stable vacuum, where the matrix eigenvalues are equally distributed on both sides of the potential. The 0A theory is described by a quiver matrix model.

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arXiv2003

Unitary and Complex Matrix Models as 1-d Type 0 Strings

We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter coupled to super-Liouville theory. We examine in detail the $\hat c=0$ or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on $(2, 4k)$ super-minimal models.

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arXiv2000

Space/Time Non-Commutativity and Causality

Field theories based on non-commutative spacetimes exhibit very distinctive nonlocal effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional Hamiltonian evolution. To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity. In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted. These field theories are evidently inconsistent and violate causality and unitarity. On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity. This raises the question of whether they also lead to acausal behavior. We show that this is not the case. Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

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arXiv2000

Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory

Searching for space/time noncommutativity we reconsider open strings in a constant background electric field. The main difference between this situation and its magnetic counterpart is that here there is a critical electric field beyond which the theory does not make sense. We show that this critical field prevents us from finding a limit in which the theory becomes a field theory on a noncommutative spacetime. However, an appropriate limit toward the critical field leads to a novel noncritical string theory on a noncommutative spacetime.

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arXiv1999

More Comments on String Theory on AdS_3

We clarify a number of issues regarding the worldsheet and spacetime descriptions of string propagation on AdS_3. We construct the vertex operators of spacetime current algebra and spacetime (super) Virasoro generators in the full interacting SL(2) WZW theory and study their Ward identities. We also explain the relation between the analysis in this note and some recent work on this subject.

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arXiv1998

Comments on String Theory on $AdS_3$

We study string propagation on $AdS_3$ times a compact space from an ``old fashioned'' worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the conjectured $AdS$/CFT correspondence for this case in the full string theory. Our results have implications for the extreme IR limit of the $D1-D5$ system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy.

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arXiv1997

Light-Cone Description of (2,0) Superconformal Theories in Six Dimensions

We study the (2,0) superconformal theories in six dimensions, which arise from the low-energy limit of k coincident 5-branes, using their discrete light-cone formulation as a superconformal quantum mechanical sigma model. We analyze the realization of the superconformal symmetry in the quantum mechanics, and the realization of primary operators. As an example we compute the spectrum of chiral primary states in symmetric Spin(5)_R representations. To facilitate the analysis we introduce and briefly discuss a new class of Lorentz non-invariant theories, which flow in the IR to the (2,0) superconformal field theories but differ from them in the UV.

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arXiv1997

Matrix Description of Interacting Theories in Six Dimensions

We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the moduli space of $N$ instantons in $\IR^4$.

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arXiv1997

Instantons, Scale Invariance and Lorentz Invariance in Matrix Theory

In this paper we consider features of graviton scattering in Matrix theory compactified on a 2-torus. The features which interest us can only be determined by nonperturbative effects in the corresponding 2+1 dimensional super Yang Mills theory. We show that the superconformal symmetry of strongly coupled Super Yang Mills Theory in 2+1 dimensions almost determines low energy, large impact parameter ten dimensional graviton scattering at zero longitudinal momentum in the Matrix model of IIB string theory. We then show that amplitudes involving arbitrary transverse momentum transfer are governed by instanton processes similar to the Polchinski Pouliot process. Finally we consider the influence of instantons on a conjectured nonrenormalization theorem. This theorem is violated by instanton processes. Far from being a problem, this fact is seen to be crucial to the consistency of the IIB interpretation. We suggest that the SO(8) invariance of strongly coupled SYM theory may lead to a proof of eleven dimensional Lorentz invariance.

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arXiv1997

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions

We consider general aspects of N=2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U(1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to ``mirror symmetries'' of 3d N=4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU(N_c) gauge groups with N_f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.

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arXiv1997

Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces

We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of nontrivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with nontrivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the ``del Pezzo contractions'' and occur at higher codimension walls of the Kähler cone.

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arXiv1996

Mirror Symmetry in Three Dimensional Gauge Theories

We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $ADE$ gauge group. In particular, we show that in three dimensions small $E_8$ instantons in string theory are described by a local quantum field theory.

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arXiv1996

SUSY Gauge Dynamics and Singularities of 4d N=1 String Vacua

Many N=1 heterotic string compactifications exhibit physically mysterious singularities at codimension one in the moduli space of vacua. At these singularities, Yukawa couplings of charged fields develop poles as a function of the moduli. We explain these conformal field theory singularities, in a class of examples, as arising from non-perturbative gauge dynamics of non-perturbative gauge bosons (whose gauge coupling is the sigma model coupling) in the string theory.

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arXiv1996

The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD

We analyze in detail the moduli space of vacua of N=2 SUSY QCD with n_c colors and n_f flavors. The Coulomb branch has submanifolds with non-Abelian gauge symmetry. The massless quarks and gluons at these vacua are smoothly connected to the underlying elementary quarks and gluons. Upon breaking N=2 by an N=1 preserving mass term for the adjoint field the theory flows to N=1 SUSY QCD. Some of the massless quarks and gluons on the moduli space of the N=2 theory become the magnetic quarks and gluons of the N=1 theory. In this way we derive the duality in N=1 SUSY QCD by identifying its crucial building blocks---the magnetic degrees of freedom---using only semiclassical physics and the non-renormalization theorem.

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arXiv1996

Comments on String Dynamics in Six Dimensions

We discuss the singularities in the moduli space of string compactifications to six dimensions with $N=1$ supersymmetry. Such singularities arise from either massless particles or non-critical tensionless strings. The points with tensionless strings are sometimes phase transition points between different phases of the theory. These results appear to connect all known $N=1$ supersymmetric six-dimensional vacua.

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arXiv1995

New N=2 Superconformal Field Theories in Four Dimensions

New examples of N=2 supersymmetric conformal field theories are found as fixed points of SU(2) N=2 supersymmetric QCD. Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and Higgs branches are understood in terms of the general structure of relevant deformations of non-trivial N=2 conformal field theories. The spectrum of scaling dimensions found are all those compatible with relevant deformations of a y^2 = x^3 singular curve.

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arXiv1995

Chiral Rings, Singularity Theory and Electric-Magnetic Duality

We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between them depends on non-trivial facts about polynomial equations, i.e.\ singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges ``trivial'' classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.

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