Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories

Within the AdS/CFT correspondence we use multicentre D3-brane metrics to investigate Wilson loops and compute the associated heavy quark-antiquark potentials for the strongly coupled SU(N) super-Yang-Mills gauge theory, when the gauge symmetry is broken by the expectation values of the scalar fields. For the case of a uniform distribution of D3-branes over a disc, we find that there exists a maximum separation beyond which there is no force between the quark and the antiquark, i.e. the screening is complete. We associate this phenomenon with the possible existence of a mass gap in the strongly coupled gauge theory. In the finite-temperature case, when the corresponding supergravity solution is a rotating D3-brane solution, there is a class of potentials interpolating between a Coulombic and a confining behaviour. However, above a certain critical value of the mass parameter, the potentials exhibit a behaviour characteristic of statistical systems undergoing phase transitions. The physical path preserves the concavity property of the potential and minimizes the energy. Using the same rotating-brane solutions, we also compute spatial Wilson loops, associated with the quark-antiquark potential in models of three-dimensional gauge theories at zero temperature, with similar results.Comment: 27 pages, latex, 7 figures; v2: no substantial changes, version to appear in Adv. Theor. Math. Phy

Self-Dual Strings and Stability of BPS States in N=2 SU(2) Gauge Theories

We show how BPS states of supersymmetric SU(2) Yang-Mills with matter -both massless and massive- are described as self-dual strings on a Riemann surface. This connection enables us to prove the stability and the strong coupling behaviour of these states. The Riemann surface naturally arises from type-IIB Calabi-Yau compactifications whose three-branes wrapped around vanishing two-cycles correspond to one-cycles on this surface.Comment: 27 LaTex with figs., Some changes in W-boson decay discussion, Refs. adde

Periods, Coupling Constants and Modular Functions in N=2 SU(2) SYM with Massive Matter

We determine the mass dependence of the coupling constant for N=2 SYM with N_f=1,2,3 and 4 flavours. All these cases can be unified in one analytic expression, given by a Schwarzian triangle function. Moreover we work out the connection to modular functions which enables us to give explicit formulas for the periods. Using the form of the J-functions we are able to determine in an elegant way the couplings and monodromies at the superconformal points.Comment: Some changes, final version to appear in IJMPA. 14 LaTex page

PP-waves from rotating and continuously distributed D3-branes

We study families of PP-wave solutions of type-IIB supergravity that have (light-cone) time dependent metrics and RR five-form fluxes. They arise as Penrose limits of supergravity solutions that correspond to rotating or continuous distributions of D3-branes. In general, the solutions preserve sixteen supersymmetries. On the dual field theory side these backgrounds describe the BMN limit of N=4 SYM when some scalars in the field theory have non-vanishing expectation values. We study the perturbative string spectrum and in several cases we are able to determine it exactly for the bosons as well as for the fermions. We find that there are special states for particular values of the light-cone constant P_+.Comment: 23 pages, Latex. v2: a few extra remarks and aesthetic changes, version to appear in JHE

Riemann surfaces and Schrodinger potentials of gauged supergravity

Supersymmetric domain-wall solutions of maximal gauged supergravity are classified in 4, 5 and 7 dimensions in the presence of non-trivial scalar fields taking values in the coset SL(N, R)/SO(N) for N=8, 6 and 5 respectively. We use an algebro-geometric method based on the Christoffel-Schwarz transformation, which allows for the characterization of the solutions in terms of Riemann surfaces whose genus depends on the isometry group. The uniformization of the curves can be carried out explicitly for models of low genus and results into trigonometric and elliptic solutions for the scalar fields and the conformal factor of the metric. The Schrodinger potentials for the quantum fluctuations of the graviton and scalar fields are derived on these backgrounds and enjoy all properties of supersymmetric quantum mechanics. Special attention is given to a class of elliptic models whose quantum fluctuations are commonly described by the generalized Lame potential \mu(\mu+1)P(z) + \nu(\nu+1)P(z+\omega_1)+ \kappa(\kappa+1)P(z+\omega_2) + \lambda(\lambda+1)P(z+\omega_1 +\omega_2) for the Weierstrass function P(z) of the underlying Riemann surfaces with periods 2\omega_1 and 2\omega_2, for different half-integer values of the coupling constants \mu, \nu, \kappa, \lambda.Comment: 13 pages, latex; contribution to the proceedings of the TMR meeting "Quantum Aspects of Gauge Theories, Supersymmetry and Unification" held in Paris in September 199

Domain walls of gauged supergravity, M-branes, and algebraic curves

We provide an algebraic classification of all supersymmetric domain wall solutions of maximal gauged supergravity in four and seven dimensions, in the presence of non-trivial scalar fields in the coset SL(8,R)/SO(8) and SL(5,R)/SO(5) respectively. These solutions satisfy first-order equations, which can be obtained using the method of Bogomol'nyi. From an eleven-dimensional point of view they correspond to various continuous distributions of M2- and M5-branes. The Christoffel-Schwarz transformation and the uniformization of the associated algebraic curves are used in order to determine the Schrodinger potential for the scalar and graviton fluctuations on the corresponding backgrounds. In many cases we explicitly solve the Schrodinger problem by employing techniques of supersymmetric quantum mechanics. The analysis is parallel to the construction of domain walls of five-dimensional gauged supergravity, with scalar fields in the coset SL(6,R)/SO(6), using algebraic curves or continuous distributions of D3-branes in ten dimensions. In seven dimensions, in particular, our classification of domain walls is complete for the full scalar sector of gauged supergravity. We also discuss some general aspects of D-dimensional gravity coupled to scalar fields in the coset SL(N,R)/SO(N).Comment: 46 pages, latex. v2: typos corrected and some references added. v3: minor corrections and improvements, references added, to appear in ATM

The three-dimensional BF Model with Cosmological Term in the Axial Gauge

We quantize the three-dimensional $BF$-model using axial gauge conditions. Exploiting the rich symmetry-structure of the model we show that the Green-functions correspond to tree graphs and can be obtained as the unique solution of the Ward-Identities. Furthermore, we will show that the theory can be uniquely determined by symmetry considerations without the need of an action principle.Comment: one reference added, transmission errors correcte

Integrability and maximally helicity violating diagrams in n=4 supersymmetric yang-mills theory.

We apply maximally helicity violating (MHV) diagrams to the derivation of the one-loop dilatation operator of N=4 supersymmetric Yang-Mills theory in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularization. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions