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

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

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

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

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

Current correlators and AdS/CFT away from the conformal point

Using the AdS/CFT correspondence we study vacua of N=4 SYM for which part of the gauge symmetry is broken by expectation values of scalar fields. A specific subclass of such vacua can be analyzed with gauged supergravity and the corresponding domain wall solutions lift to continuous distributions of D3-branes in type IIB string theory. Due to the non-trivial expectation value of the scalars, the SO(6) R-symmetry is spontaneously broken and field theory predicts the existence of Goldstone bosons. We explicitly show that, in the dual supergravity description, these emerge as massless poles in the current two-point functions, while the bulk gauge fields which are dual to the broken currents become massive via the Higgs mechanism. We find agreement with field theory expectations and, hence, provide a non-trivial test of the AdS/CFT correspondence far away from the conformal point.Comment: 12 pages, Latex. Contribution to the proceedings of the 7th Hellenic summer school and Workshops on High Energy Physics, Corfu, Greece, 13 Aug.-13 Sept. 200

On running couplings in gauge theories from type-IIB supergravity

We construct an explicit solution of type-IIB supergravity describing the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling with an ultraviolet stable fixed point corresponding to the N=4 SU(N) super-Yang-Mills theory at large N. The running coupling has a power law behaviour, argued to be universal, that is consistent with holography. Around the critical point, our solution defines an asymptotic expansion for the gauge coupling beta-function. We also calculate the first correction to the Coulombic quark-antiquark potential.Comment: 10 pages, latex, v2: Another form of the solution is given and a reference is added, v3: a reference is added, final form to appear in PL

Twisted N=4 SUSY Algebra in Topological Models of Schwarz Type

We reinvestigate the twisted N=4 supersymmetry present in Schwarz type topological field models. We show that Chern-Simons theory in three dimensions can be untwisted to a kind of sigma-model with reversed statistics only in the free case. By dimensional reduction we define then the two-dimensional BF-model. We establish an analog result concerning the untwisting. As a consequence of the definition through dimensional reduction we find new fermionic scalar symmetries that have been overlooked so far in the literature.Comment: 12 pages, no figure, Late

On Asymptotic Freedom and Confinement from Type-IIB Supergravity

We present a new type-IIB supergravity vacuum that describes the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling such that the theory becomes asymptotically free in the ultraviolet. It also has a running theta angle due to a non-vanishing axion field in the supergravity solution. We also present a worm-hole solution, which has finite action per unit four-dimensional volume and two asymptotic regions, a flat space and an AdS^5\times S^5. The corresponding N=2 gauge theory, instead of being finite, has a running coupling. We compute the quark-antiquark potential in this case and find that it exhibits, under certain assumptions, an area-law behaviour for large separations.Comment: 9 pages, latex, 1 figure v2: minor aesthetic changes v3: some scale factors corrected, version to appear in PL

MHV Lagrangian for N=4 Super Yang-Mills

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.Comment: 17 pages 4 figures, 2 sections and several references added typo correcte