7 research outputs found
Self-consistency of Conformally Coupled ABJM Theory at the Quantum Level
We study the superconformal Chern-Simons matter field theory
(the ABJM theory) conformally coupled to a Lorentzian, curved background
spacetime. To support rigid supersymmetry, such backgrounds have to admit
twistor spinors. At the classical level, the symmetry of the theory can be
described by a conformal symmetry superalgebra. We show that the full
superconformal algebra persists at the quantum level using the
BV-BRST method
Background independence in gauge theories
Classical field theory is insensitive to the split of the field into a
background configuration and a dynamical perturbation. In gauge theories, the
situation is complicated by the fact that a covariant (w.r.t. the background
field) gauge fixing breaks this split independence of the action. Nevertheless,
background independence is preserved on the observables, as defined via the
BRST formalism, since the violation term is BRST exact. In quantized gauge
theories, however, BRST exactness of the violation term is not sufficient to
guarantee background independence, due to potential anomalies. We define
background independent observables in a geometrical formulation as flat
sections of the observable algebra bundle over the manifold of background
configurations, with respect to a flat connection which implements background
variations. A theory is then called background independent if such a flat
(Fedosov) connection exists. We analyze the obstructions to preserve background
independence at the quantum level for pure Yang-Mills theory and for
perturbative gravity. We find that in the former case all potential
obstructions can be removed by finite renormalization. In the latter case, as a
consequence of power-counting non-renormalizability, there are infinitely many
non-trivial potential obstructions to background independence. We leave open
the question whether these obstructions actually occur.Comment: v2: Corrections in the proof in Sect. 3.3.3, references added; v3:
published versio
A Lagrangian constraint analysis of first order classical field theories with an application to gravity
We present a method that is optimized to explicitly obtain all the
constraints and thereby count the propagating degrees of freedom in (almost
all) manifestly first order classical field theories. Our proposal uses as its
only inputs a Lagrangian density and the identification of the a priori
independent field variables it depends on. This coordinate-dependent, purely
Lagrangian approach is complementary to and in perfect agreement with the
related vast literature. Besides, generally overlooked technical challenges and
problems derived from an incomplete analysis are addressed in detail. The
theoretical framework is minutely illustrated in the Maxwell, Proca and
Palatini theories for all finite spacetime dimensions. Our novel
analysis of Palatini gravity constitutes a noteworthy set of results on its
own. In particular, its computational simplicity is visible, as compared to
previous Hamiltonian studies. We argue for the potential value of both the
method and the given examples in the context of generalized Proca and their
coupling to gravity. The possibilities of the method are not exhausted by this
concrete proposal.Comment: 44 pages, 1 figure. v2: references added; journal versio
Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity
Based on spherically symmetric reduction of loop quantum gravity,
quantization of the portion interior to the horizon of a Reissner-Nordstr\"{o}m
black hole is studied. Classical phase space variables of all regions of such a
black hole are calculated for the physical case . This calculation
suggests a candidate for a classically unbounded function of which all
divergent components of the curvature scalar are composed. The corresponding
quantum operator is constructed and is shown explicitly to possess a bounded
operator. Comparison of the obtained result with the one for the Swcharzschild
case shows that the upper bound of the curvature operator of a charged black
hole reduces to that of Schwarzschild at the limit . This
local avoidance of singularity together with non-singular evolution equation
indicates the role quantum geometry can play in treating classical singularity
of such black holes.Comment: To be appeared in International Journal of Theoretical Physic
Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory