arXiv subjects
Publications and source records attributed to M. Bertolini.
We report on some recent results within the string/gauge theory correspondence, both in the conformal and in the non conformal cases, for a recently found class of N=1 dual pairs. These results provide the first cross check of AdS/CFT and field theory techniques like a-maximization. Moreover, they furnish new examples of cascading gauge theories and the first instance of 4d dynamical supersymmetry breaking embedded in the correspondence
We study the IR dynamics of the cascading non-conformal quiver theory on N regular and M fractional D3 branes at the tip of the complex cone over the first del Pezzo surface. The horizon of this cone is the irregular Sasaki-Einstein manifold Y^{2,1}. Our analysis shows that at the end of the cascade supersymmetry is dynamically broken.
We review in a pedagogical manner some of the efforts aiming to extend the gauge/gravity correspondence to non-conformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific examples: fractional D-branes on orbifolds and D-branes wrapped on supersymmetric cycles of Calabi-Yau spaces. We explore in particular which gauge theory information can be extracted from the corresponding supergravity solutions, and what the remaining open problems are. We also briefly explain the connection between these and other approaches, such as fractional branes on conifolds, branes suspended between branes, M5-branes on Riemann surfaces and M-theory on G2-holonomy manifolds, and discuss the role played by geometric transitions in all that.
We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional $N$=1 SCFT with irrational R-charges. The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface. By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges. Our results perfectly match with those inherited from the recently discovered supergravity dual background. Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface. This should flow to a SCFT with irrational charges, too. All of our results differ from previous findings in the literature and outline interesting subtleties in a-maximization and AdS/CFT techniques overlooked in the past.
Microphotoluminescence mapping experiments were performed on a modulation doped (Cd,Mn)Te quantum well exhibiting carrier induced ferromagnetism. The zero field splitting that reveals the presence of a spontaneous magnetization in the low-temperature phase, is measured locally; its fluctuations are compared to those of the spin content and of the carrier density, also measured spectroscopically in the same run. We show that the fluctuations of the carrier density are the main mechanism responsible for the fluctuations of the spontaneous magnetization in the ferromagnetic phase, while those of the Mn spin density have no detectable effect at this scale of observation.
The spectroscopic properties of a spin polarized two-dimensional hole gas are studied in modulation doped (Cd,Mn)Te quantum wells. The giant Zeeman effect induces a significant spin splitting even at very small values of the applied field. Several methods of measuring the carrier density (Hall effect, filling factors of the Landau levels at high field, various manifestations of Moss-Burstein shifts) are described and calibrated. The value of the spin splitting needed to fully polarize the hole gas, evidences a strong enhancement of the spin susceptibility of the hole gas due to carrier-carrier interaction. At small values of the spin splitting, whatever the carrier density (non zero) is, photoluminescence lines are due to the formation of charged excitons in the singlet state. Spectral shifts in photoluminescence and in transmission (including an "excitonic Moss-Bustein shift") are observed and discussed in terms of excitations of the partially or fully polarized hole gas. At large spin splitting, and without changing the carrier density, the singlet state of the charged exciton is destabilized in favour of a triplet state configuration of holes. The binding energy of the singlet state is thus measured and found to be independent of the carrier density (in contrast with the splitting between the charged exciton and the neutral exciton lines). The state stable at large spin splitting is close to the neutral exciton at low carrier density, and close to an uncorrelated electron-hole pair at the largest values of the carrier density achieved. The triplet state gives rise to a characteristic double-line structure with an indirect transition to the ground state (with a strong phonon replica) and a direct transition to an excited state of the hole gas.
We present a study of p-type doping of CdTe and Cd$_{1-x}$Mn$_x$Te quantum wells from surface states. We show that this method is as efficient as usual modulation doping with nitrogen acceptors, and leads to hole densities exceeding $2 \times 10^{11}$ cm$^{-2}$. Surface doping was successfully applied to obtain carrier-induced ferromagnetism in a Cd$_{1-x}$Mn$_x$Te quantum well. The observed temperature dependence of photoluminescence spectra, and the critical temperature, correspond well to those previously reported for ferromagnetic quantum wells doped with nitrogen.
We refine the dictionary of the gauge/gravity correspondence realizing N=1 super Yang-Mills by means of D5-branes wrapped on a resolved Calabi-Yau space. This is done by fixing an ambiguity on the correct interpretation of the holographic dual of the running gauge coupling and amounts to identify a specific 2-cycle in the dual ten-dimensional supergravity background. In doing so, we also discuss the role played in this context by gauge transformations in the relevant seven-dimensional gauged supergravity. While all nice properties of the duality are maintained, this modification of the dictionary has some interesting physical consequences and solves a puzzle recently raised in the literature. In this refined framework, it is also straightforward to see how the correspondence naturally realizes a geometric transition.
We find a new Penrose limit of AdS_5*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 AdS_5*S^5/Z_M, 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.
In this note we show how the anomalies of both pure and matter coupled N=1,2 supersymmetric gauge theories describing the low energy dynamics of fractional branes on orbifolds can be derived from supergravity.
We construct non-extremal fractional D-brane solutions of type-II string theory at the Z_2 orbifold point of K3. These solutions generalize known extremal fractional-brane solutions and provide further insights into N=2 supersymmetric gauge theories and dual descriptions thereof. In particular, we find that for these solutions the horizon radius cannot exceed the non-extremal enhancon radius. As a consequence, we conclude that a system of non-extremal fractional branes cannot develop into a black brane. This conclusion is in agreement with known dual descriptions of the system.
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.
A strong influence of illumination and electric bias on the Curie temperature and saturation value of the magnetization is demonstrated for semiconductor structures containing a modulation-doped p-type Cd0.96Mn0.04Te quantum well placed in various built-in electric fields. It is shown that both light beam and bias voltage generate an isothermal and reversible cross-over between the paramagnetic and ferromagnetic phases, in the way that is predetermined by the structure design. The observed behavior is in quantitative agreement with the expectations for systems, in which ferromagnetic interactions are mediated by the weakly disordered two-dimensional hole liquid.
This is a pedagogical and extended version of the results published in Refs. [1,2] and presented by the authors in various talks during the last year. We discuss the type II D-branes (both regular and fractional) of the orbifold R^{1,5}*R^4/Z_2, we determine their corresponding supergravity solution and show how this can be used to study the properties of N=2 super Yang-Mills. Supergravity is able to reproduce the perturbative moduli space of the gauge theory, while it does not encode the non-perturbative corrections. The short distance region of space-time, which corresponds to the infrared region of the gauge theory, is excised by an enhancon mechanism, and more states should be included in the low energy effective action in order to enter inside the enhancon and recover the instanton corrections. (To be published on a Memorial Volume commemorating Michael Marinov)
We study a bound state of fractional D3/D7-branes in the ten-dimensional space R^{1,5}*R^{4}/Z_2 using the boundary state formalism. We construct the boundary actions for this system and show that higher order terms in the twisted fields are needed in order to satisfy the zero-force condition. We then find the classical background associated to the bound state and show that the gauge theory living on a probe fractional D3-brane correctly reproduces the perturbative behavior of a four-dimensional N=2 supersymmetric gauge theory with fundamental matter.
We construct a new family of classical BPS solutions of type IIB supergravity describing 3-branes transverse to a 6-dimensional space with topology R^2*ALE. They are characterized by a non-trivial flux of the supergravity 2-forms through the homology 2-cycles of a generic smooth ALE manifold. Our solutions have two Killing spinors and thus preserve N=2 supersymmetry. They are expressed in terms of a quasi harmonic function H (the ``warp factor''), whose properties we study in the case of the simplest ALE, namely the Eguchi-Hanson manifold. The equation for H is identified as an instance of the confluent Heun equation. We write explicit power series solutions and solve the recurrence relation for the coefficients, discussing also the relevant asymptotic expansions. While, as in all such N=2 solutions, supergravity breaks down near the brane, the smoothing out of the vacuum geometry has the effect that the warp factor is regular in a region near the cycle. We interpret the behavior of the warp factor as describing a three-brane charge ``smeared'' over the cycle and consider the asymptotic form of the geometry in that region, showing that conformal invariance is broken even when the complex type IIB 3-form field strength is assumed to vanish. We conclude with a discussion of the basic features of the gauge theory dual.
We study the classical geometry associated to fractional D3-branes of type IIB string theory on R^4/Z_2 which provide the gravitational dual for N=2 super Yang-Mills theory in four dimensions. As one can expect from the lack of conformal invariance on the gauge theory side, the gravitational background displays a repulson-like singularity. It turns out however, that such singularity can be excised by an enhancon mechanism. The complete knowledge of the classical supergravity solution allows us to identify the coupling constant of the dual gauge theory in terms of the string parameters and to find a logarithmic running that is governed precisely by the beta-function of the N=2 super Yang-Mills theory.
We review recent results in the study of regular four dimensional BPS black holes in toroidally compactified type II (or M) theory. We discuss the generating solution for this kind of black holes, its microscopic description(s), and compute the corresponding microscopic entropy. These achievements, which provide a description of the fundamental degrees of freedom accounting for the entropy of any regular BPS black hole in the theory under consideration, are inscribed within a research project aimed to the study of the microscopic properties of this kind of solutions in relation to U--duality invariants computed on the corresponding macroscopic (supergravity) description.