Jacob Sonnenschein

Wilson Loops in the Large N Limit at Finite Temperature

Using a proposal of Maldacena we compute in the framework of the supergravity description of N coincident D3 branes the energy of a quark anti-quark pair in the large N limit of U(N) N=4 SYM in four dimensions at finite temperature.

Holographic melting and related properties of mesons in a quark-gluon plasma

We analyze mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic considerations imply that large-spin mesons do not experience drag effects when moving through the quark-gluon plasma. They do, however, have a maximum velocity for fixed spin, beyond which they dissociate.

Wilson loops, confinement, and phase transitions in large N gauge theories from supergravity

We use the recently proposed supergravity approach to large N gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite temperature do not admit phase transitions between the weakly coupled super Yang Mills and supergravity regimes. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at finite temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase transition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.

potential from strings in curved space-time – classical results ☆

Abstract We compute the leading behaviour of the quark–anti-quark potential from a generalized Nambu–Goto action associated with a curved space-time having an “extra dimension”. The extra dimension can be the radial coordinate in the AdS/CFT correspondence, the Liouville field in Polyakovs approach, or an internal dimension in MQCD. In particular, we derive the condition for confinement, and in the case it occurs we find the string tension and the correction to the linear potential.

Probing flavored mesons of confining gauge theories by supergravity

We incorporate massive flavored fundamental quarks in the supergravity dual of = 1 SYM by introducing D7 brane probes to the Klebanov Strassler background. We find probe configurations that solve the D7 equations of motion. We compute the quadratic fluctuations of the D7 brane and extract the spectrum of vector and pseudo scalar flavored mesons. The spectra found are discrete and exhibit a mass gap of the order of the glueball mass.

Regge trajectories for mesons in the holographic dual of large-N(c) QCD

We discuss Regge trajectories of dynamical mesons in large-Nc QCD, using the supergravity background describing Nc D4-branes compactified on a thermal circle. The flavor degrees of freedom arise from the addition of Nf << Nc D6 probe branes. Our work provides a string theoretical derivation, via the gauge/string correspondence, of a phenomenological model describing the meson as rotating point-like massive particles connected by a flux string. The massive endpoints induce nonlinearities for the Regge trajectory. For light quarks the Regge trajectories of mesons are essentially linear. For massive quarks our trajectories qualitatively capture the nonlinearity detected in lattice calculations.

On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories

We give a simple proof of the relation AanF = &bl (Tr #2), which is vaiid for N = 2 super-symmetric QCD with massless quarks. We consider SU( NC) gauge theories as well as SO( NC) and SP ( NC). An analogous relation which corresponds to massive hypermultiplets is written down. We also discuss the generalizations to N = 1 models in the Coulomb phase.

Gauge fixing and renormalization in topological quantum field theory

Abstract We show how Wittens topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero.

Comments on the M theory approach to N = 1 SQCD and brane dynamics

Abstract We use the M theory approach of Witten to investigate N = 1 SU( N c ) SQCD with N f flavors. We reproduce the field theoretical results and identify in M theory the gluino condensate and the eigenvalues of the meson matrix. This approach allows us to identify the constant piece of the effective field theory coupling from which the coefficient of the one-loop β-function can be identified. By studying the area of the M-theory five-brane we investigate the stability of type IIA brane configurations. We prove that in a supersymmetric setup there is no force between static D4-branes that end on NS five-branes. The force in the case that there is a relative velocity between the branes is computed. We show that at the regions of intersecting IIA branes the curvature of the M theory five-brane is singular in the type IIA limit.

M-theory and Seiberg-Witten curves: orthogonal and symplectic groups

We discuss N = 2 supersymmetric type IIA brane configurations within M-theory. This is a generalization of the work of Witten to all classical groups. (~) 1997 Published by Elsevier Science B.V.