879 research outputs found
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 times toric
Sasaki-Einstein seven-manifolds. In the large 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
superconformal field theory to a pure Chern-Simons theory on
the 3-manifold. On the other hand, it leads to a warped AdS 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 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 scaling behavior and are proportional
to the volume of the 3-manifold, while the three-loop and higher terms are
suppressed at large . 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
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