Linear Quivers and N=1 SCFTs from M5-branes

We study a class of N=1 quiver gauge theories build out of vector multiplets and matter multiplets in the fundamental and bifundamental representations. We argue that these theories flow to interacting SCFTs in the IR and calculate their central charges. We exhibit a type IIA brane construction which at low energies is described by these SCFTs. This also leads to a natural description of the theories in terms of M5-branes on a punctured sphere.Comment: 21 pages, 5 figure

Universal RG Flows Across Dimensions and Holography

We study RG flows between superconformal field theories living in different spacetime dimensions which exhibit universal properties, independent of the details of the UV and IR theories. In particular, when the UV and IR theories are both even-dimensional we establish exact universal relations between their conformal anomaly coefficients. We also provide strong evidence for similar relations between appropriately defined free energies for RG flows between odd-dimensional theories in the large $N$ limit. Holographically, these RG flows across dimensions are described by asymptotically AdS black branes in a gauged supergravity theory, which we exhibit explicitly. We also discuss the uplift of these solutions to string and M-theory and comment on how the entropy of such black branes is captured by the dual field theory.Comment: 64 pages, 2 figures; v2: additional comments and references, typos fixe

Comments on Squashed-sphere Partition Functions

We study the partition function of odd-dimensional conformal field theories placed on spheres with a squashed metric. We establish that the round sphere provides a local extremum for the free energy which, in general, is not a global extremum. In addition, we show that the leading quadratic correction to the free energy around this extremum is proportional to the coefficient, $C_T$, determining the two-point function of the energy-momentum tensor in the CFT. For three-dimensional CFTs, we compute explicitly this proportionality constant for a class of squashing deformations which preserve an $SU(2)\times U(1)$ isometry group on the sphere. In addition, we evaluate the free energy as a function of the squashing parameter for theories of free bosons, free fermions, as well as CFTs holographically dual to Einstein gravity with a negative cosmological constant. We observe that, after suitable normalization, the dependence of the free energy on the squashing parameter for all these theories is nearly universal for a large region of parameter space and is well approximated by a simple quadratic function arising from holography. We generalize our results to five-dimensional CFTs and, in this context, we also study theories holographically dual to six-dimensional Gauss-Bonnet gravity.Comment: 40 pages, 7 figures, 1 table; v2: additional comments and clarifications added, updated bibliograph

(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

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

Spherical Branes

We construct new solutions of ten-dimensional supergravity with sixteen supercharges which describe the backreaction of D$p$-branes with spherical worldvolume. These solutions are holographically dual to the $(p+1)$-dimensional maximally supersymmetric Yang-Mills theory on $S^{p+1}$. The finite size of the sphere provides an IR cut-off for the gauge theory which is manifested in the supergravity solution as a smooth cap-off of the geometry. In the UV the size of the sphere plays no role and the backgrounds asymptote to the well-known supergravity solutions that describe the near-horizon limit of flat D$p$-branes. We compute the on-shell action of our spherical brane solutions and show that it is in agreement with recent supersymmetric localization results for the free energy of maximal SYM theory on $S^{p+1}$.Comment: 57 pages, 4 figures; v2: minor corrections, appendix adde

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