(0,2) SCFTs from the Leigh-Strassler Fixed Point

We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.Comment: 40 pages, 6 figure

BV-Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of (W-) Strings

Given a simple, simply laced, complex Lie algebra \bfg corresponding to the Lie group $G$, let \bfnp be the subalgebra generated by the positive roots. In this paper we construct a BV-algebra \fA[\bfg] whose underlying graded commutative algebra is given by the cohomology, with respect to \bfnp, of the algebra of regular functions on $G$ with values in \mywedge (\bfnp\backslash\bfg). We conjecture that \fA[\bfg] describes the algebra of {\it all} physical (i.e., BRST invariant) operators of the noncritical \cW[\bfg] string. The conjecture is verified in the two explicitly known cases, \bfg=\sltw (the Virasoro string) and \bfg=\slth (the \cW_3 string).Comment: 10 pages, Typeset in TeX (with amssym.def input

Mass-deformed ABJM and Black Holes in AdS4_4

We find a class of new supersymmetric dyonic black holes in four-dimensional maximal gauged supergravity which are asymptotic to the ${\rm SU(3)}\times {\rm U(1)}$ invariant AdS$_4$ Warner vacuum. These black holes can be embedded in eleven-dimensional supergravity where they describe the backreaction of M2-branes wrapped on a Riemann surface. The holographic dual description of these supergravity backgrounds is given by a partial topological twist on a Riemann surface of a three-dimensional $\mathcal{N}=2$ SCFT that is obtained by a mass-deformation of the ABJM theory. We compute explicitly the topologically twisted index of this SCFT and show that it accounts for the entropy of the black holes.Comment: 67 pages, 7 figure

Supersymmetric Janus Solutions in Four Dimensions

We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the world-volume of multiple M2-branes. We study three classes of examples in which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$ supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$ vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. In eleven dimensions, this $G_2$ to $G_2$ solution corresponds to a domain wall across which a magnetic flux reverses orientation.Comment: 54 pages, 11 figure