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.
122852309
THE GOLDSTONE THEOREM AT TWO LOOPS FROM AN ALGEBRAIC IDENTITY
We give an explicit demonstration of the Goldstone theorem at the level of two-loop Feynman graphs in the spontaneously broken O(2) linear σ model by showing that the integrands of the 1PI "pion" self-energy graphs cancel each other at zero momentum as a consequence of the identity m2[k2(k2+m2)]−1 = k−2− (k2+m2)−1. The proof holds for any regularization scheme which respects this identity.
102305181
The matrix theory S matrix
The technology required for eikonal scattering amplitude calculations in Matrix theory is developed. Using the entire supersymmetric completion of the v 4 /r 7 Matrix theory potential we compute the graviton–graviton scattering amplitude and find agreement with eleven
21071347
Non-Einstein source effects in massive gravity
We exhibit novel effects (absent in GR) of sources in massive gravity. First, we show that removing its ghost mode forces a field-current identity: The metric’s trace is locally proportional to that of its stress tensor; a point source implies a metric singularity enhanced by the square of the graviton’s range. Second, exterior solutions acquire spatial stress hair—their metric components depend on the interior T_(ij). Also, in contrast to naive expectations, the Newtonian potential of a source is now determined by both its spatial stress and mass. Our explicit results are obtained at linear, Fierz–Pauli, level but qualitatively persist nonlinearly.
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.
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.