A Dielectric Flow Solution with Maximal Supersymmetry

We obtain a solution to eleven-dimensional supergravity that consists of M2-branes embedded in a dielectric distribution of M5-branes. Contrary to normal expectations, this solution has maximal supersymmetry for a brane solution (i.e. sixteen supercharges). While the solution is constructed using gauged supergravity in four dimensions, the complete eleven-dimensional solution is given. In particular, we obtain the Killing spinors explicitly, and we find that they are characterised by a duality rotation of the standard Dirichlet projection matrix for M2-branes.Comment: 17 pages; harvma

The boundary sine-Gordon theory: classical and semi-classical analysis

We consider the sine-Gordon model on a half-line, with an additional potential term of the form $-M\cos{\beta\over 2}(\varphi-\varphi_0)$ at the boundary. We compute the classical time delay for general values of $M$, $\beta$ and $\varphi_0$ using $\tau$-function methods and show that in the classical limit, the method of images still works, despite the non-linearity of the problem. We also perform a semi-classical analysis, and find agreement with the exact quantum S-matrix conjectured by Ghoshal and Zamolodchikov.Comment: 19 pages, 5 figures. Preprint USC-94-013. (Numerical mistake corrected.

BPS Geodesics in N=2 Supersymmetric Yang-Mills Theory

We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric $ds^2 = |\lambda_{SW}|^2$. Because the existence of such geodesics implies the existence of BPS states in N=2 supersymmetric Yang-Mills theory, one can use these methods to study the BPS spectrum in various phases of the Yang-Mills theory. By way of illustration, we show how, using our new methods, one can easily recover the known results for the N=2 supersymmetric SU(2) pure gauge theory, and we show in detail how it also works for the N=2, SU(2) theory coupled to a massive adjoint matter multiplet.Comment: 23 pages, harvmac, epsf, 8 figure

Instanton Expansions for Mass Deformed N=4 Super Yang-Mills Theories

We derive modular anomaly equations from the Seiberg-Witten-Donagi curves for softly broken N=4 SU(n) gauge theories. From these equations we can derive recursion relations for the pre-potential in powers of m^2, where m is the mass of the adjoint hypermultiplet. Given the perturbative contribution of the pre-potential and the presence of ``gaps'' we can easily generate the m^2 expansion in terms of polynomials of Eisenstein series, at least for relatively low rank groups. This enables us to determine efficiently the instanton expansion up to fairly high order for these gauge groups, e. g. eighth order for SU(3). We find that after taking a derivative, the instanton expansion of the pre-potential has integer coefficients. We also postulate the form of the modular anomaly equations, the recursion relations and the form of the instanton expansions for the SO(2n) and E_n gauge groups, even though the corresponding Seiberg-Witten-Donagi curves are unknown at this time.Comment: harvmac(b) 28 page

On the Algebraic Structure of Gravitational Descendants in CP(n-1) Coset Models

We investigate how specific free-field realizations of twisted N=2 supersymmetric coset models give rise to natural extensions of the ``matter'' Hilbert spaces in such a manner as to incorporate the various gravitational excitations. In particular, we show that adopting a particular screening prescription is equivalent to imposing the requisite equivariance condition on cohomology. We find a simple algebraic characterization of the $W_n$-gravitational ground ring spectra of these theories in terms of affine-$SU(n)$ highest weights..Comment: 12p, harvmac/lanlmac with hyperlinks, 1 uuencoded PostScript figure, CERN-TH.7442/94, USC-94/01

Non-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves

We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to \IT^2 compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper subsectors of the full string theory, which can be consistently decoupled. In this way we obtain rigid effective theories that have an intrinsically stringy BPS spectrum. Geometrically the moduli spaces correspond to special geometry of certain non-compact Calabi-Yau spaces of an intriguing form. An equivalent description can be given in terms of Seiberg-Witten curves, given by the elliptic simple singularities together with a peculiar choice of meromorphic differentials. We speculate that the moduli spaces describe non-perturbative non-critical string theories.Comment: 29 pages, harvmac, 1 figure, minor correction

Exact solution of a massless scalar field with a relevant boundary interaction

We solve exactly the "boundary sine-Gordon" system of a massless scalar field \phi with a \cos[\beta\phi/2] potential at a boundary. This model has appeared in several contexts, including tunneling between quantum-Hall edge states and in dissipative quantum mechanics. For \beta^2 < 8\pi, this system exhibits a boundary renormalization-group flow from Neumann to Dirichlet boundary conditions. By taking the massless limit of the sine-Gordon model with boundary potential, we find the exact S matrix for particles scattering off the boundary. Using the thermodynamic Bethe ansatz, we calculate the boundary entropy along the entire flow. We show how these particles correspond to wave packets in the classical Klein-Gordon equation, thus giving a more precise explanation of scattering in a massless theory.Comment: 23 pages, USC-94-1

Boundary states, matrix factorisations and correlation functions for the E-models

The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E_6 using conformal field theory methods, thereby enabling us to test results recently obtained in this context.Comment: 20 pages, no figure

Boundary Action of N=2 Super-Liouville Theory

We derive a boundary action of N=2 super-Liouville theory which preserves both N=2 supersymmetry and conformal symmetry by imposing explicitly $T={\bar T}$ and $G={\bar G}$. The resulting boundary action shows a new duality symmetry.Comment: 15 pages; One reference is adde

Notes On The S-Matrix Of Bosonic And Topological Non-Critical Strings

We show that the equivalence between the c=1 non-critical bosonic string and the N=2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts $H_3^+$ correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2)/U(1) coset at level n>1, which has been argued recently to be equivalent with a c<1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT.Comment: harvmac, 22 pages; v2 typos corrected, version appearing in JHE