QCD string from D0 branes

We report the results of a set of high precision simulations performed in the 3d gauge Ising model. We evaluated the interquark potential and the first few energy levels and compared them with the predictions obtained with the effective Nambu-Goto string and with the free bosonic string. The data are precise enough to unambiguously distinguish between the free string predictions and those obtained using the N-G effective string. At large distances we find a remarkable agreement between Monte Carlo data and N-G predictions for the first excited energy level, while the free string picture is definitely excluded. As the interquark distance is decreased (and/or the finite temperature becomes higher) the Monte Carlo results show larger and larger deviations both from the N-G and from the free string predictions. In order to better understand this behaviour we re-derived the effective Nambu-Goto theory result for the Polyakov loop correlator using a covariant quantization. We chose as boundary conditions those of an open string attached to two D0-branes at spatial distance R, in a target space with compact euclidean time. Obviously our treatment is fully consistent only in d = 26. The extension to generic d requires taking into account the Liouville mode of Polyakov’s formulation. The analogy with the standard light cone calculation suggests that the contribution due to the Liouville field can be neglected for large R. At shorter scales, the Liouville mode cannot be neglected and its contribution to the interquark potential might be the source of the discrepancies with respect to the effective N-G results that we observe in our Monte Carlo simulations

Non-perturbative aspects of gauge/gravity duality

Recently we provided a microscopic derivation of the exact supergravity profile for the twisted scalar field emitted by systems of fractional D3-branes at a Z2 orbifold singularity. In this contribution we focus on a set-up supporting an N = 2 SYM theory with SU(2) gauge group and Nf=4. We take into account the tower of D-instanton corrections to the source terms for the twisted scalar and find that its profile can be expressed in terms of the chiral ring elements of the gauge theory. We show how the twisted scalar, which at the perturbative level represents the gravity counterpart of the gauge coupling, at the non-perturbative level is related to the effective gauge coupling in an interestingly modified way.Comment: 13 pages, 1 figure. Proceedings of the Corfu Summer Institute 2012 "School and Workshops on Elementary Particle Physics and Gravity", September 8-27, 2012, Corfu, Greece. Luca Giacone was the speaker. v2: two references added, one reference update

Instantons in N=2 magnetized D-brane worlds

In a toroidal orbifold of type IIB string theory we study instanton effects in N=2 super Yang-Mills theories engineered with systems of wrapped magnetized D9 branes and Euclidean D5 branes. We analyze the various open string sectors in this brane system and study the 1-loop amplitudes described by annulus diagrams with mixed boundary conditions, explaining their role in the stringy instanton calculus. We show in particular that the non-holomorphic terms in these annulus amplitudes precisely reconstruct the appropriate Kahler metric factors that are needed to write the instanton correlators in terms of purely holomorphic variables. We also explicitly derive the correct holomorphic structure of the instanton induced low energy effective action in the Coulomb branch.Comment: 40 pages, 5 figures, JHEP class. Some footnotes added and typos corrected. Version published in JHE

High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model

Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation.Comment: 20 pages, 1 figur

Instanton effects in N=1 brane models and the Kahler metric of twisted matter

We consider locally consistent systems of magnetized D9 branes on an orbifolded six-torus which support N=1 gauge theories. In such realizations, the matter multiplets arise from "twisted" strings connecting different stacks of branes. The introduction of Euclidean 5 branes (E5) wrapped on the six-dimensional compact space leads to instanton effects. For instance, if the system is engineered so as to yield SQCD, a single E5 brane may account for the ADS/TVY superpotential. We discuss the subtle interplay that exists between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy action of the N=1 theory. The consistency of this picture allows to obtain information on the Kahler metric of the chiral matter multiplets arising from twisted strings.Comment: 33 pages, 4 figures. V2: improved discussion, clarifyng comments and references added. Version to be published in JHE

Boundary states for moving D-branes

We determine the boundary state for both the NS-NS and R-R sectors of superstring theory. We show how they are modified under a boost. The boosted boundary state is then used for computing the interaction of two D-branes moving with constant velocity reproducing with a completely different method a recent calculation by Bachas.Comment: 10 pages, LaTeX, no figures; Eqs. (47) and (48) correcte

Boundary States for GS superstrings in an Hpp wave background

We construct the boundary states preserving half the global supersymmetries in string theory propagating on a Hpp background.Comment: 13 pages, latex2e with JHEP3.0 class, no figures. V1: clarified the status of branes not sitting at the origin and added a constraint which boundary states must satisf

The partition function of interfaces from the Nambu-Goto effective string theory

We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.Comment: 28 pages, 4 figure

The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study

The limiting procedure of special Kahler manifolds to their rigid limit is studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of certain singularities. In two examples we consider all the periods in and around the rigid limit, identifying the nontrivial ones in the limit as periods of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler potential of the special Kahler manifold reduces to that of a rigid special Kahler manifold. We extensively make use of the structure of these Calabi-Yau manifolds as K3 fibrations, which is useful to obtain the periods even before the K3 degenerates to an ALE manifold in the limit. We study various methods to calculate the periods and their properties. The development of these methods is an important step to obtain exact results from supergravity on Calabi-Yau manifolds.Comment: 79 pages, 8 figures. LaTeX; typos corrected, version to appear in Classical and Quantum Gravit

On the effective string spectrum of the tridimensional Z(2) gauge model

We study the Z(2) lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop correlation function, which is measured in the 3d Ising spin system using duality. This allows us to perform a stringent comparison with the predictions of effective string models. We find a remarkable agreement between the numerical estimates and the Nambu-Goto predictions for the energy gaps at intermediate and large distances. The precision of our data allows to distinguish clearly between the predictions of the full Nambu-Goto action and the simple free string model up to an interquark distance $r \approx 10/\sqrt{\sigma}$. At the same time, our results also confirm the breakdown of the effective picture at short distances, supporting the hypothesis that terms which are not taken into account in the usual Nambu-Goto string formulation yield a non-trivial shift to the energy levels. Furthermore, we discuss the theoretical implications of these results.Comment: 31 pages, 14 figure