50856545
BPS black holes, quantum attractor flows and automorphic forms
We propose a program for counting microstates of four-dimensional BPS black holes in N{>=}2 supergravities with symmetric-space valued scalars by exploiting the symmetries of timelike reduction to three dimensions. Inspired by the equivalence between the four-dimensional attractor flow and geodesic flow on the three-dimensional scalar manifold, we radially quantize stationary, spherically symmetric BPS geometries. Connections between the topological string amplitude, attractor wave function, the Ooguri-Strominger-Vafa conjecture and the theory of automorphic forms suggest that black hole degeneracies are counted by Fourier coefficients of modular forms for the three-dimensional U-duality group, associated to special unipotent representations which appear in the supersymmetric Hilbert space of the quantum attractor flow.
16066542
Spinors on manifolds with boundary: APS index theorems with torsion
Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS η invariant in the presence of torsion. The bulk contribution must also be modified and is computed using a supersymmetric quantum mechanics representation. Here we find agreement with existing results which employed heat kernel and Pauli-Villars techniques. Nonetheless, this computation also provides a stringent check of the Feynman rules of de Boer et al. for the computation of quantum mechanical path integrals. Our results can be verified via a duality relation between manifolds admitting a Killing-Yano tensor and manifolds with torsion. As an explicit example, we compute the indices of Taub-NUT and its dual constructed using this method and find agreement for any finite radius to the boundary. We also suggest a resolution to the problematic appearance of the Nieh-Yan invariant multiplied by the regulator (mass) 2 in computations of the chiral gravitational anomaly coupled to torsion.
119103201
A continuous Wick rotation for spinor fields and supersymmetry in Euclidean space
We obtain a continuous Wick rotation for Dirac, Majorana and Weyl spinors $\psi \to \exp ({1\over 2} \theta \gamma^4 \gamma^5)\psi$ which interpolates between Minkowski and Euclidean field theories.
118704552
Massive higher spins from BRST and tractors
Abstract We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit systems manifest. In this approach, physical models are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive models can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk–boundary correspondence.
7032725
Matrix theory and Feynman diagrams
We briefly review the computation of graviton and antisymmetric tensor scattering amplitudes in Matrix Theory from a diagramatic S-Matrix point of view.
15701670
D = 11 SUGRA as the low energy effective action of matrix theory: three form scattering
We employ the LSZ reduction formula for matrix theory introduced in our earlier work to compute the t-pole S-matrix for three form--three form scattering. The result agrees completely with tree level D = 11 SUGRA. Taken together with previous results on graviton-graviton scattering this shows that matrix theory indeed reproduces the bosonic sector of the D = 11 SUGRA action including the Chern-Simons term. Furthermore we provide a detailed account of our framework along with the technology to compute any matrix theory one-loop t-pole scattering amplitude at vanishing p− exchange.
119317491
Is Quantum Gravity a Chern{Simons Theory?
We propose a model of quantum gravity in arbitrary dimensions dened in terms of the BV quantization of a supersymmetric, innite dimensional matrix model. This gives an (AKSZ-type) Chern{Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert spaceH. The model is motivated by previous attempts to formulate gravity in terms of non-commutative, phase space, eld theories as well as the Feerman{ Graham curved analog of Dirac spaces for conformally invariant wave equations. The eld
11049353
Covariant constraints for generic massive gravity and analysis of its characteristics
We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates 5 degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. The constraint’s covariant expression permits computation of the model’s caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.