Alberto Lerda

CLASSICAL p-BRANES FROM BOUNDARY STATE ∗

We show that the boundary state description of a Dp-brane is strictly related to the corresponding classical solution of the low-energy string effective action. By projecting the boundary state on the massless states of the closed string we obtain the tension, the R-R charge and the large-distance behavior of the classical solution. We discuss both the case of a single D-brane and that of bound states of two D-branes. We also show that in the R-R sector the boundary state, written in a picture which treats asymmetrically the left and right components, directly yields the R-R gauge potentials.

Classical gauge instantons from open strings

We study the D3/D(-1) brane system and show how to compute instanton corrections to correlation functions of gauge theories in four dimensions using open string techniques. In particular we show that the disks with mixed boundary conditions that are typical of the D3/D(-1) system are the sources for the classical instanton solution. This can then be recovered from simple calculations of open string scattering amplitudes in the presence of D-instantons. Exploiting this fact we also relate this stringy description to the standard instanton calculus of field theory.

N=2 gauge theories on systems of fractional D3/D7 branes

We study a bound state of fractional D3/D7-branes in the ten-dimensional space R1,5×R4/Z2 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.

MICROSCOPIC STRING ANALYSIS OF THE D0-D8 BRANE SYSTEM AND DUAL R-R STATES

Abstract Using the boundary state formalism, we perform a microscopic string analysis of the interaction between two D-branes and provide a local interpretation for the R-R force in the D0–D8 brane system. To do so, we construct BRST invariant vertex operators for the massless R-R states in the asymmetric picture that are proportional to potentials rather than field strengths. The Hilbert space of such R-R states contains combinations of two vectors that decouple from all physical amplitudes, even in the presence of boundaries. Identifying these vectors, we remove the null states and recover duality relations among R-R potentials. If we specify to the D0–D8 brane system, this mechanism implies that the R-R 1-form state has a non-zero overlap with both the D0-brane and the D8-brane, thus explaining from a local point of view the non-vanishing R-R contribution in the interaction for the D0–D8 brane system and those related to it by duality.

Stringy instantons at orbifold singularities

We study the effects produced by D-brane instantons on the holomorphic quantities of a D-brane gauge theory at an orbifold singularity. These effects are not limited to reproducing the well known contributions of the gauge theory instantons but also generate extra terms in the superpotential or the prepotential. On these brane instantons there are some neutral fermionic zero-modes in addition to the ones expected from broken supertranslations. They are crucial in correctly reproducing effects which are dual to gauge theory instantons, but they may make some other interesting contributions vanish. We analyze how orientifold projections can remove these zero-modes and thus allow for new superpotential terms. These terms contribute to the dynamics of the effective gauge theory, for instance in the stabilization of runaway directions.

Fractional D-branes and their gauge duals

We study the classical geometry associated to fractional D3-branes of type IIB string theory on 42 which provide the gravitational dual for = 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 β function of the = 2 super Yang-Mills theory.

Instanton Calculus In R-R Background And The Topological String

We study a system of fractional D3 and D(-1) branes in a Ramond-Ra- mond closed string background and show that it describes the gauge instantons of N = 2 super Yang-Mills theory and their interactions with the graviphoton of N = 2 supergravity. In particular, we analyze the instanton moduli space using string the- ory methods and compute the prepotential of the effective gauge theory exploiting the localization methods of the instanton calculus showing that this leads to the same information given by the topological string. We also comment on the relation between our approach and the so-called -background.

N=1 and N=2 super-Yang–Mills theories from wrapped branes☆

We consider supergravity solutions of D5-branes wrapped on supersymmetric 2-cycles and use them to discuss relevant features of four-dimensional N=1 and N=2 super-Yang–Mills theories with gauge group SU(N). In particular in the N=1 case, using a gravitational dual of the gaugino condensate, we obtain the complete NSVZ β-function. We also find non-perturbative corrections associated to fractional instantons with charge 2/N. These non-perturbative effects modify the running of the coupling constant which remains finite even at small scales in a way that resembles to the soft confinement scenario of QCD.

STABLE NON-BPS STATES IN STRING THEORY: A PEDAGOGICAL REVIEW

We present a pedagogical review of the stable non-BPS states in string theory which have recently attracted some attention in the literature. In particular, following the analysis of A. Sen, we discuss in detail the case of the stable non-BPS D-particle of Type I theory whose existence is predicted (and required) by the heterotic/Type I duality. We show that this D-particle originates from an unstable bound state formed by a D1/anti-D1 pair of Type IIB in which the tachyon field acquires a solitonic kink configuration. The mechanism of tachyon condensation is discussed first at a qualitative level and then with an exact conformal field theory analysis.

Stable non-BPS D-branes in type I string theory

Abstract We use the boundary state formalism to study, from the closed string point of view, superpositions of branes and anti-branes which are relevant in some non-perturbative string dualities. Treating the tachyon instability of these systems as proposed by Sen, we show how to incorporate the effects of the tachyon condensation directly in the boundary state. In this way we manage to show explicitly that the D1–anti-D1 pair of Type I is a stable non-BPS D-particle, and compute its mass. We also generalize this construction to describe other non-BPS D-branes of Type I. By requiring the absence of tachyons in the open string spectrum, we find which configurations are stable and compute their tensions. Our classification is in complete agreement with the results recently obtained using the K-theory of space-time.