14701289
Four – Dimensional BPS Black Holes : Macroscopic and Microscopic Correspondence
I review some recent results in the study of regular four dimensional BPS black holes in toroidally compactified type II string (or M) theory. One of these achievements consists in having written the generating solution of 1/8 BPS black holes in the N=8 theory in a form which could be easily described by suitable configurations of D-branes in the weak string coupling regime of both type IIA and IIB theories. The microscopic parameters characterizing these configurations have been related in a precise way to the supergravity (macroscopic) parameters of the solution. This achievement opens up the possibility of systematically studying the microscopic properties of any regular BPS black hole solution of the N=8 theory. O ne of the main issues of the “second string revolution” (1995) is the concept of string dualities which provided a new insight into the non–perturbative side of the known superstring theories. These dualities are mappings between regimes of different superstring theories (some of them have been verified while other just conjectured). Their existence naturally induces to consider the known superstring theories as perturbative realizations on different backgrounds of a fundamental theory of gravity (FTG) whose general formulation however is still missing. It is known that the low energy limit of superstring theory is described by supergravity. Although supergravity in this picture is regarded just as a macroscopic theory, it is expected to possess important informations about the FTG. Indeed, it has been argued [1] that the largest (continuous) global symmetry group U of the supergravity field equations and Bianchi identities at classical level should encode the definition, as a suitable discrete group U(Z), of the conjectured superstring U–duality, namely the ultimate duality connecting all superstring theories realized on various backgrounds. This duality is thus expected to be an exact symmetry of the FTG. Unfortunately not much is known about the group U(Z), starting from the very definition and its action on superstring states. On the other hand the action of the group U on the supergravity solutions is, in principle, known. A fundamental role in probing superstring dualities has been played so far by the BPS black hole solutions of supergravity. These solutions are characterized by the property of preserving a fraction of the original supersymmetries, and this feature protects their physical quantities, to a certain extent, from quantum corrections. As a consequence of their supersymmetry, BPS black holes in supergravity are expected to correspond to exact solutions of superstring theory. The BPS condition moreover is U–duality invariant. This allows to characterize these supergravity solutions within orbits of the continuous U–duality group, defined by a certain number ofU–invariants {Ik} (e.g. the entropy). All the physical properties of the BPS solutions entering a same U– duality orbit are expected to be encoded in the Non–Perturbative Quantum Effects 2000 M. Bertolini and M. Trigiante corresponding generating solution. The generating solution of BPS black holes is defined, within a certain supergravity theory, as the solution depending on the least number of parameters such that the invariants {Ik} are free for a certain choice of the boundary conditions. As a consequence of its definition, by acting on the generating solution by means of U one recovers the whole U–duality orbit. A suitable discrete set of points within this orbit should correspond to superstring black holes (non–perturbative solutions) connected by the action of U(Z) and which therefore represent different descriptions of a same solution within the FTG (see figure below). The Fundamental Theory U U(Z) Macro-Micro Correspondence ( ) Generating Solution ( ) Classical Supergravity. Superstring Theories microscopic degrees of freedom described by the FTG are indeed related to invariants of the group U(Z). Pinpointing the exact correspondence between the macroscopic (supergravity) and microscopic descriptions (e.g. in terms of D–branes in a suitable regime) of a generating solution, one would in principle be able to study systematically the microscopic realization of a generic solution in the same orbit. Moreover this could be the first step in order to unravel the action of U(Z) on stringy objects in higher dimensions and to ultimately deduce their fundamental degrees of freedom. Here we review some recent results in the study of four dimensional regular BPS black holes within toroidally compactified type II superstring (or M) theory. The relevant low–energy description for these solutions is four dimensionalN = 8 supergravity. In section 1 we shall start addressing the question: how much can we learn at classical supergravity level about the microscopic description of a BPS solution? A possible answer will lead us to discuss a mathematical analysis carried out in [2] which provides an intrinsic group theoretical characterization of the scalar and vector fields in the D = 4, N = 8 theory in terms of dimensionally reduced type II fields. The geometrical framework so defined turns out to provide the convenient “laboratory” in which to systematically study the microscopic descriptions of BPS solutions and their duality relations. Using these tools one can then characterize R– R charged generating solutions of regular BPS black holes as elements of a suitable equivalence class defined with respect to the action of S and T dualities. This result is discussed in section 2 and allows us to formulate the precise correspondence, worked out in [3], between the parameters defining two T –dual R–R charged microscopic descriptions (in type IIA and IIB settings) of the generating solution and the supergravity quantities related to its macroscopic description. This final goal is dealt with in section 3. 1. Supergravity Laboratory. The only prediction which may be drawn at classical supergravity level on the microscopic description of a BPS solution is clearly limited just to the background fields which couple to it. This can be done for instance by associating each superstring scalar and vector zero–mode with quantities intrinsic to the U–duality group of the low– energy supergravity (see [4, 2]). The D = 4, N = 8 supergravity is a maximally extended supersymmetric theory, i.e. it has 32 supercharges. Its bosonic sector consists of the graviton, 70 scalar fields, spanning the homogeneous manifold Mscal = E7(7)/SU(8), and 28 vector fields. The latter are related to a vector of 56 quantized charges (p, qΣ), which transforms in the Sp(56) of E7(7), and a central charge matrix ZAB entering the local realization on the moduli space of the supersymmetry algebra and transforming in the 28 of SU(8). The former charges are moduli–independent and should be regarded just as supergravity parameters, while the latter are moduli dependent and are related to the physical charges, i.e. the actual charges
11360961
Fractional branes and N=1 gauge theories
We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group with matter in the bifundamental. In particular, when only one type of brane is present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes to the bulk fields and present the corresponding supergravity solution, valid at large distances. By using a probe analysis, we are able to obtain the Wilsonian beta-function for those gauge theories that possess some chiral multiplet. Although, due to the lack of moduli, the probe technique is not directly applicable to the case of pure N=1 Yang-Mills, we point out that the same formula gives the correct result also for this case.
5405891
Gauge theory description of compactified pp-waves
We find a new Penrose limit of AdS5 × S 5 that gives the maximally symmetric pp-wave background of Type IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N = 4 SYM theory. The new Penrose limit, when applied to AdS5 ×S 5 /ZM, yields a pp-wave with a space-like circle. The dual gauge theory description involves a triple scaling limit of an N = 2 quiver gauge theory. We present in detail the map between gauge theory operators and string theory states including winding states, and verify agreement between the energy eigenvalues obtained from string theory and those computed in gauge theory, at least to one-loop order in the planar limit. We furthermore consider other related new Penrose limits and explain how these limits can be understood as part of a more general framework.
16559651
N=2 cascade revisited and the enhancon bearings
Supergravity backgrounds with varying fluxes generated by fractional branes at nonisolated Calabi-Yau singularities had escaped a precise dual field theory interpretation so far. In the present work, considering the prototypical example of such models, the CxC{sup 2}/Z{sub 2} orbifold, we propose a solution for this problem, and show that the known cascading solution corresponds to a vacuum on the Coulomb branch of the corresponding quiver gauge theory involving a sequence of strong coupling transitions reminiscent of the baryonic root of N=2 supersymmetric quantum chromodynamics . We also find a slight modification of this cascading vacuum which upon mass deformation is expected to flow to the Klebanov-Strassler cascade. Finally, we discuss an infinite class of vacua on the Coulomb branch whose renormalization group flows include infinitely coupled conformal regimes, and explain their gravitational manifestation in terms of new geometric structures that we dub enhancon bearings. Repulson-free backgrounds dual to all the vacua we analyze are explicitly provided.
119203512
Dynamical completions of generalized O’Raifeartaigh models
A bstractWe present gauge theory completions of Wess-Zumino models admitting supersymmetry breaking vacua with spontaneously broken R-symmetry. Our models are simple deformations of generalized ITIY models, a supersymmetric theory with gauge group Sp(N), N +1 flavors plus singlets, with a modified tree level superpotential which explicitly breaks (part of) the global symmetry. Depending on the nature of the deformation, we obtain effective O’Raifeartaigh-like models whose pseudomoduli space is locally stable in a neighborhood of the origin of field space, or in a region not including it. Hence, once embedded in direct gauge mediation scenarios, our models can give low energy spectra with either suppressed or unsuppressed gaugino mass.
8372258
The Generating solution of regular N=8 BPS black holes
In this paper we construct the five-parameter generating solution of N = 8 BPS regular supergravity black holes as a five-parameter solution of the N = 2 STU model. Our solution has a simpler form with respect to previous constructions which have already appeared in the literature and moreover, through the embedding [SL(2)]3 SU(3,3) E7(7) discussed in previous papers, the action of the U-duality group is well defined. This allows us to reproduce via U-duality rotations any other solution, such as those corresponding to R-R black holes whose microscopic description is given by intersecting D-branes.
28988576
Hybrid conformal field theories
A bstractWe describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kähler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of linear models and comparing spectra among the phases.
54042308
Accidents in (0,2) Landau-Ginzburg theories
A bstractWe study the role of accidental symmetries in two-dimensional (0,2) superconformal field theories obtained by RG flow from (0,2) Landau-Ginzburg theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) Landau-Ginzburg models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. We also give a self-contained discussion of aspects of (0,2) conformal perturbation theory.
118374856
Massless spectrum for hybrids CFTs
We describe a class of theories obtained by fibering a Landau-Ginburg orbifold over a compact Kaehler base. While such theories are often described as phases of some GLSM, our description is independent of such an embedding. We provide a method for computing the massless spectrum. This note is based on the longer paper arXiv:1307.7063.
43843434
Worldsheet instantons and (0,2) linear models
A bstractWe study the stability of heterotic compactifications described by (0,2) gauged linear sigma models with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten [1]. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of linear models for which a vanishing theorem holds, generating an extensive list of consistent heterotic backgrounds.