arXiv subjects

David Berenstein

Publications and source records attributed to David Berenstein.

At least 127 records · Page 7Linked to original sources

arXiv2002

Reverse geometric engineering of singularities

One can geometrically engineer supersymmetric field theories theories by placing D-branes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a noncommutative quiver algebra which is constructed from the quiver diagram and the superpotential. The center of this noncommutative algebra is a commutative algebra, which is the ring of holomorphic functions on a variety V. If certain algebraic conditions are met, then the reverse geometric engineering produces V as the geometry that D-branes probe. It is also argued that the identification of V is invariant under Seiberg dualities.

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arXiv2001

On the universality class of the conifold

The possibility of having discrete degrees of freedom at singularities associated to `conifolds with discrete torsion' is studied. We find that the field theory of D-brane probes near these singularities is identical to ordinary conifolds, so that there are no additional discrete degrees of freedom located at the singularity. We shed light on how the obstructions to resolving the singularity are global topological issues rather that local obstrucions at the singularity itself. We also analyze the geometric transitions and duality cascades when one has fractional branes at the singularity and compute the moduli space of an arbitrary number of probes in the geometry. We provide some evidence for a conjecture that there are no discrete degrees of freedom localized at any Calabi-Yau singularity that can not be guessed from topological data away from the singularity.

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arXiv2001

Resolution of Stringy Singularities by Non-commutative Algebras

In this paper we propose a unified approach to (topological) string theory on certain singular spaces in their large volume limit. The approach exploits the non-commutative structure of D-branes, so the space is described by an algebraic geometry of non-commutative rings. The paper is devoted to the study of examples of these algebras. In our study there is an auxiliary commutative algebraic geometry of the center of the (local) algebras which plays an important role as the target space geometry where closed strings propagate. The singularities that are resolved will be the singularities of this auxiliary geometry. The singularities are resolved by the non-commutative algebra if the local non-commutative rings are regular. This definition guarantees that D-branes have a well defined K-theory class. Homological functors also play an important role. They describe the intersection theory of D-branes and lead to a formal definition of local quivers at singularities, which can be computed explicitly for many types of singularities. These results can be interpreted in terms of the derived category of coherent sheaves over the non-commutative rings, giving a non-commutative version of recent work by M. Douglas. We also describe global features like the Betti numbers of compact singular Calabi-Yau threefolds via global holomorphic sections of cyclic homology classes.

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arXiv2001

The Standard Model on a D-brane

We present a consistent string theory model which reproduces the Standard Model, consisting of a D3-brane at a simple orbifold singularity. We study some simple features of the phenomenology of the model. We find that the scale of stringy physics must be in the multi-TeV range. There are natural hierarchies in the fermion spectrum and there are several possible experimental signatures of the model.

hep-ph↗

arXiv2001

Observations on non-commutative field theories in coordinate space

We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field theories, with or without supersymmetry. The formalism has a number of intuitive advantages. First it makes clear the appearance of new degrees of freedom in the infrared. Second, it allows for a study of correlation functions of (composite) operators. Thus we calculate the two point function in position space of the insertion of certain composite operators. We demonstrate that, even at tree level, many of the by now familiar properties of non-commutative field theories are manifest and have simple interpretations. The form of correlation functions are such that certain singularities may be interpreted in terms of dimensional reduction along the non-commutative directions: this comes about because these are theories of fundamental dipoles.

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arXiv2000

D-branes on Singularities: New Quivers from Old

In this paper we present simplifying techniques which allow one to compute the quiver diagrams for various D-branes at (non-Abelian) orbifold singularities with and without discrete torsion. The main idea behind the construction is to take the orbifold of an orbifold. Many interesting discrete groups fit into an exact sequence $N\to G\to G/N$. As such, the orbifold $M/G$ is easier to compute as $(M/N)/(G/N)$ and we present graphical rules which allow fast computation given the $M/N$ quiver.

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arXiv2000

Non-Commutative Calabi-Yau Manifolds

We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We consider two examples: a toroidal orbifold T^6/Z_2 x Z_2, and an orbifold of the quintic in CP_4, each with discrete torsion. The non-commutative geometry tools are enough to describe various properties of the orbifolds. First, one describes correctly the fractionation of branes at singularities. Secondly, for the first example we show that one can recover explicitly a large slice of the moduli space of complex structures which deform the orbifold. For this example we also show that we get the correct counting of complex structure deformations at the orbifold point by using traces of non-commutative differential forms (cyclic homology).

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arXiv2000

Non-Commutative Moduli Spaces, Dielectric Tori and T-duality

We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the D-brane bubbles. Different regions of moduli space are associated with D5-branes of various topologies; singularities in the moduli space are associated with topology change. T-duality on toroidal topologies maps between mirror string realizations of the field theory.

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arXiv2000

Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua

We study marginal and relevant supersymmetric deformations of the N=4 super-Yang-Mills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F-term constraints. These field theories are dual to superstring theories propagating on deformations of the AdS_5xS^5 geometry. We study D-branes propagating in these vacua and introduce the appropriate notion of algebraic geometry for non-commutative spaces. The resulting moduli spaces of D-branes have several novel features. In particular, they may be interpreted as symmetric products of non-commutative spaces. We show how mirror symmetry between these deformed geometries and orbifold theories follows from T-duality. Many features of the dual closed string theory may be identified within the non-commutative algebra. In particular, we make progress towards understanding the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric tensor of the string is turned on, and we shed light on some aspects of discrete anomalies based on the non-commutative geometry.

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arXiv2000

Discrete Torsion, AdS/CFT and duality

We analyse D-branes on orbifolds with discrete torsion, extending earlier results. We analyze certain Abelian orbifolds of the type C^3/ Γ, where Γis given by Z_m x Z_n, for the most general choice of discrete torsion parameter. By comparing with the AdS/CFT correspondence, we can consider different geometries which give rise to the same physics. This identifies new mirror pairs and suggests new dualities at large N. As a by-product we also get a more geometric picture of discrete torsion.

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arXiv1999

Quantization of Superstrings in Ramond-Ramond Backgrounds

We present a perturbative study of Ramond-Ramond backgrounds in the NSR formalism. We show how to perform sigma-model computations and discuss in detail the structure of the BRST charge and picture-changing operators. Contact terms play a vital role in the analysis. We also give evidence for a two loop non-renormalization theorem for the background beta functions.

hep-th↗

arXiv1999

Spacetime supersymmetry in $AdS_3$ backgrounds

We construct string target spacetimes with AdS_3 x X geometry, which have an N=2 spacetime superconformal algebra. X is found to be a U(1) fibration over a manifold which is a target for an N=2 worldsheet conformal field theory. We emphasize theories with free field realizations where in principle it is possible to compute the full one-particle string spectrum.

hep-th↗

arXiv1999

Superstring Perturbation Theory and Ramond-Ramond Backgrounds

We consider perturbative Type II superstring theory in the covariant NSR formalism in the presence of NSNS and RR backgrounds. A concrete example that we have in mind is the geometry of D3-branes which in the near-horizon region is AdS_5 x S_5, although our methods may be applied to other backgrounds as well. We show how conformal invariance of the string path integral is maintained order by order in the number of holes. This procedure makes uses of the Fischler-Susskind mechanism to build up the background geometry. A simple formal expression is given for a σ-model Lagrangian. This suggests a perturbative expansion in 1/g^2N and 1/N. As applications, we consider at leading order the mixing of RR and NSNS states, and the realization of the spacetime supersymmetry algebra.

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arXiv1998

String Junctions and Bound States of Intersecting Branes

We study four-dimensional black hole configurations which result from wrapping M5-branes on a Calabi-Yau manifold, as well as U-dual realizations. Our aim is to understand the microscopic degrees of freedom responsible for the existence of bound states of multiple branes. The details depend on the chosen U-frame; in some cases, they are massless string junctions. We also identify a perturbative description in which these states correspond to twisted strings of intersecting D3-branes at an orbifold singularity. In each case, these are the preponderant states of the spacetime infrared conformal field theory and account for the entropy of the blackhole.

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arXiv1998

The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit

The operator product expansion for ``small'' Wilson loops in {\cal N}=4, d=4 SYM is studied. The OPE coefficients are calculated in the large N and g_{YM}^2 N limit by exploiting the AdS/CFT correspondence. We also consider Wilson surfaces in the (0,2), d=6 superconformal theory. In this case, we find that the UV divergent terms include a term proportional to the rigid string action.

hep-th↗

arXiv1998

Matrix Theory on ALE Spaces and Wrapped Membranes

We study the properties of wrapped membranes in matrix theory on ALE spaces. We show that the only BPS bound states of wrapped membranes that can form are roots of the $A$-$D$-$E$ group. We determine a bound on the energy of a bound state and find the correct dependence on the blow-up parameters and longitudinal momentum expected from M-Theory. For the $A_{n-1}$ series, we construct explicit classical solutions for the wrapped membrane bound states. These states have a very rich structure and have a natural interpretation in terms of noncommutative geometry. In the $A_1$ case, we examine the spectrum of excitations around the wrapped membrane solution and provide an explicit calculation of their energies. The results agree exactly with supergravity calculations.

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arXiv1997

Aspects of ALE Matrix Models and Twisted Matrix Strings

We examine several aspects of the formulation of M(atrix)-Theory on ALE spaces. We argue for the existence of massless vector multiplets in the resolved $A_{n-1}$ spaces, as required by enhanced gauge symmetry in M-Theory, and that these states might have the correct gravitational interactions. We propose a matrix model which describes M-Theory on an ALE space in the presence of wrapped membranes. We also consider orbifold descriptions of matrix string theories, as well as more exotic orbifolds of these models, and present a classification of twisted matrix string theories according to Reid's exact sequences of surface quotient singularities.

hep-th↗

arXiv1997

On the Moduli Spaces of M(atrix)-Theory Compactifications

By identifying the moduli space of coupling constants in the SYM description of toroidal compactifications of M(atrix)-Theory, we construct the M(atrix) description of the moduli spaces of Type IIA string theory compactified on T^n. Addition of theta terms to the M(atrix) SYM produces the shift symmetries necessary to recover the correct global structure of the moduli spaces. Up to n=3, the corresponding BPS charges transform under the proper representations of the U-duality groups. For n=4,5, if we make the ansatz of including the BPS charges corresponding to the wrapped M-theory 5-brane, the correspondence with Type IIA continues to hold. However, for n=6, we find additional charges for which there are no obvious candidates in M(atrix)-Theory.

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