Geometric free energy of toric AdS4/CFT3 models

We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS$_4$ times toric Sasaki-Einstein seven-manifolds. In the large $N$ limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges. The coefficients of the polynomial are determined geometrically from the toric diagrams. We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices. Decomposing the trial R-charges into mesonic and baryonic variables, and eliminating the baryonic ones, we show that the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume function. On the gravity side, we explore the possibility of using the same quartic polynomial as the prepotential in the AdS gauged supergravity. Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find perfect agreement in the mesonic sector but some discrepancy in the baryonic sector.Comment: 39 pages, 21 figures; v2. references added, minor improvement

Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes

A novel understanding of scattering amplitudes in terms of on-shell diagrams and positive Grassmannian has been recently established for four dimensional Yang-Mills theories and three dimensional Chern-Simons theories of ABJM type. We give a detailed construction of the positroid stratification of orthogonal Grassmannian relevant for ABJM amplitudes. On-shell diagrams are classified by pairing of external particles. We introduce a combinatorial aid called `OG tableaux' and map each equivalence class of on-shell diagrams to a unique tableau. The on-shell diagrams related to each other through BCFW bridging are naturally grouped by the OG tableaux. Introducing suitably ordered BCFW bridges and positive coordinates, we construct the complete coordinate charts to cover the entire positive orthogonal Grassmannian for arbitrary number of external particles. The graded counting of OG tableaux suggests that the positive orthogonal Grassmannian constitutes a combinatorial polytope.Comment: 32 pages, 23 figures; v2. minor corrections; v3. several clarifications and minor improvement

Absorption and Recoil of Fundamental String by D-String

Inclusive absorption cross section of fundamental IIB string to D-string is calculated perturbatively. The leading order result agrees with estimate based on stringy Higgs mechanism via Cremmer-Scherk coupling. It is argued that the subleading order correction is dominated by purely planar diagrams in the large mass limit. The correction represents conversion of binding energy into local recoil process of the fundamental string and D-string bound state. We show their presence explicitly in the next leading order.Comment: harvmac, 4 figures, 17 page

A new integral formula for supersymmetric scattering amplitudes in three dimensions

We propose a new integral formula for all tree-level scattering amplitudes of N=6 supersymmetric Chern-Simons theory. It resembles the Roiban-Spradlin-Volovich-Witten formula for N=4 supersymmetric Yang-Mills theory based on a twistor string theory formulation. Our formula implies that the (2k)-point tree-level amplitude is closely related to degree (k-1) curves in CP^{k-1}.Comment: 4 pages; v2. references adde

Topological Twisting of Multiple M2-brane Theory

Bagger-Lambert-Gustavsson theory with infinite dimensional gauge group has been suggested to describe M5-brane as a condensation of multiple M2-branes. Here we perform a topological twisting of the Bagger-Lambert-Gustavsson theory. The original SO(8) R-symmetry is broken to SO(3)XSO(5), where the former may be interpreted as a diagonal subgroup of the Euclidean M5-brane world-volume symmetry SO(6), while the latter is the isometry of the transverse five directions. Accordingly the resulting action contains an one-form and five scalars as for the bosonic dynamical fields. We further lift the action to a generic curved three manifold. In order to make sure the genuine topological invariance, we construct an off-shell formalism such that the scalar supersymmetry transformations are nilpotent strictly off-shell and independent of the metric of the three manifold. The one loop partition function around a trivial background yields the Ray-Singer torsion. The BPS equation involves an M2-brane charge density given by a Nambu-Goto action defined in an internal three-manifold.Comment: 20 pages, no figure; Refs added, minor improvement, to appear in JHE

Holography of Wrapped M5-branes and Chern-Simons theory

We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N^3 scaling with precise coefficients.Comment: 5 pages, 2 figures. Some clarifications, references added, misprint correcte

Holography of 3d-3d correspondence at Large N

We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an $\mathcal{N}=2$ superconformal field theory to a pure Chern-Simons theory on the 3-manifold. On the other hand, it leads to a warped AdS$_4$ geometry in M-theory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d-3d correspondence, we propose a conjecture for the large $N$ limit of the perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold. The conjecture claims that the tree, one-loop and two-loop terms all share the same $N^3$ scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large $N$. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the suppression of higher loop terms in a few examples.Comment: 37 pages, 7 figure