Conformally invariant supersymmetric field theories on Sp × S1 and super p-branes

We construct supersymmetric field theories on Sp × S1 for p = 1,…,5. These spaces are the boundaries of the anti-de Sitter space in (p + 2)-dimensions. Thesetheories are invariant under the super extension of the anti-de Sitter group in (p + 2)-dimensions, whose bosonic subalgebra is SO(p + 1,2) asterisk in circle SO(N), for N = 1,2,4,8. The anti-de Sitter group SO(p + 1,2) acts as the conformal group on Sp × S1. We conjecture that these theories describe the super p-branes propagating in AdSp + 2 × SN−1. The internal space is always one of the parallelizable spheres, namely S1, S3 or S7

On gravitational dressing of renormalization group beta-functions beyond lowest order of perturbation theory

Based on considerations in conformal gauge I derive up to nextleading order a relation between the coefficients of beta-functions in 2D renormalizable field theories before and after coupling to gravity. The result implies a coupling constant dependence of the ratio of both beta-functions beyond leading order.Comment: DESY 94-?, HU Berlin-IEP-94/21, 9 pages, Late

The Gaugings of Maximal D=6 Supergravity

We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes 16 vector fields that carry a chiral spinor representation of the duality group. We utilize the embedding tensor method which determines the appropriate combinations of these vectors that participate in gauging of a suitable subgroup of SO(5,5). The construction also introduces the magnetic duals of the 5 two-form potentials and 16 vector fields.Comment: 34 pages, latex, reference added, typo's corrected and minor improvements mad

Dualisation of Dualities, I

We analyse the global (rigid) symmetries that are realised on the bosonic fields of the various supergravity actions obtained from eleven-dimensional supergravity by toroidal compactification followed by the dualisation of some subset of fields. In particular, we show how the global symmetries of the action can be affected by the choice of this subset. This phenomenon occurs even with the global symmetries of the equations of motion. A striking regularity is exhibited by the series of theories obtained respectively without any dualisation, with the dualisation of only the Ramond-Ramond fields of the type IIA theory, with full dualisation to lowest degree forms, and finally for certain inverse dualisations (increasing the degrees of some forms) to give the type IIB series. These theories may be called the GL_A, D, E and GL_B series respectively. It turns out that the scalar Lagrangians of the E series are sigma models on the symmetric spaces K(E_{11-D})\backslash E_{11-D} (where K(G) is the maximal compact subgroup of G) and the other three series lead to models on homogeneous spaces K(G) \backslash G\semi \R^s. These can be understood from the E series in terms of the deletion of positive roots associated with the dualised scalars, which implies a group contraction. We also propose a constrained Lagrangian version of the even dimensional theories exhibiting the full duality symmetry and begin a systematic analysis of abelian duality subalgebras.Comment: Latex, 82 pages, minor corrections and references adde

Timelike Boundary Liouville Theory

The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL and its close cousin, a positive norm boson with a non-hermitian boundary interaction, arise in the description of the $c=1$ accumulation point of $c<1$ minimal models, as the worldsheet description of open string tachyon condensation in string theory and in scaling limits of superconductors with line defects. Bulk correlators are shown to be exactly soluble. In contrast, due to OPE singularities near the boundary interaction, the computation of boundary correlators is a challenging problem which we address but do not fully solve. Analytic continuation from the known correlators of spatial boundary Liouville to TBL encounters an infinite accumulation of poles and zeros. A particular contour prescription is proposed which cancels the poles against the zeros in the boundary correlator d(\o) of two operators of weight \o^2 and yields a finite result. A general relation is proposed between two-point CFT correlators and stringy Bogolubov coefficients, according to which the magnitude of d(\o) determines the rate of open string pair creation during tachyon condensation. The rate so obtained agrees at large \o with a minisuperspace analysis of previous work. It is suggested that the mathematical ambiguity arising in the prescription for analytic continuation of the correlators corresponds to the physical ambiguity in the choice of open string modes and vacua in a time dependent background.Comment: 28 pages, 1 figure, v2 reference and acknowledgement adde

Epsilon-expansion in quantum field theory in curved spacetime

We discuss epsilon-expansion in curved spacetime for asymptotically free and asymptotically non-free theories. The esistence of stable and unstable fixed points is investigated for $f \phi^4$ and SU(2) gauge theory. It is shown that epsilon-expansion maybe compatible with asymptotic freedom on special solutions of the RG equations in a special case (supersymmetric theory). Using epsilon-expansion RG technique the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL-model are found in 4-epsilon- dimensional curved space (in linear curvature approximation). The curvature- induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.Comment: Latex file, 22 pages, July 1997 preprin

Compactifications with S-Duality Twists

We consider generalised Scherk Schwarz reductions of supergravity and superstring theories with twists by electromagnetic dualities that are symmetries of the equations of motion but not of the action, such as the S-duality of D=4, N=4 super-Yang-Mills coupled to supergravity. The reduction cannot be done on the action itself, but must be done either on the field equations or on a duality invariant form of the action, such as one in the doubled formalism in which potentials are introduced for both electric and magnetic fields. The resulting theory in odd-dimensions has massive form fields satisfying a self-duality condition $dA \sim m*A$. We construct such theories in D=3,5,7.Comment: Latex, 26 pages. References adde

Lectures on Gauged Supergravity and Flux Compactifications

The low-energy effective theories describing string compactifications in the presence of fluxes are so-called gauged supergravities: deformations of the standard abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.Comment: 48 pages, lectures given at the RTN Winter School on Strings, Supergravity and Gauge Theories, CERN, January 200