The appearance of non trivial torsion for some Ricci dependent theories in the Palatini formalism

As is known from studies of gravity models in the Palatini formalism, there exist two inequivalent definitions of the generalized Ricci tensor in terms of the generalized curvature namely, Reµν = Rρµρν and Rνµ = gαβRµανβ. A deep formal investigation of theories with lagrangians of the form L = L(Re(µν)) was initiated in [4]. In that work, the authors leave the connection free, and find out that the torsion only appears as a projective mode. This agrees with the widely employed condition of vanishing torsion in these theories as a simple gauge choice. In the present work the complementary scenario is studied namely, the one described by a lagrangian that depends on the other possible Ricci tensor L = L(R(µν)). The torsion is completely characterized in terms of the metric and the connection, and a rather detailed description of the equations of motion is presented. It is shown that these theories are non trivial even for 1+1 space time dimensions, and admit non zero torsion even in this apparently simple case. It is suggested that to impose zero torsion by force may result into an incompatible system. In other words, the presence of torsion may be beneficial for insuring that the equations of motion are well posed.

Avoiding gauge ambiguities in cavity quantum electrodynamics

Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few low-lying energy eigenstates. This effect is particularly prominent in the ultra-strong coupling regime. Such ambiguities arise because transformations reshuffle the partition between light and matter degrees of freedom and so level truncation is a gauge dependent approximation. To avoid this gauge ambiguity, we redefine the electromagnetic fields in terms of potentials for which the resulting canonical momenta and Hamiltonian are explicitly unchanged by the gauge choice of this theory. Instead the light/matter partition is assigned by the intuitive choice of separating an electric field between displacement and polarisation contributions. This approach is an attractive choice in typical cavity quantum electrodynamics situations.

Building bulk geometry from the tensor Radon transform

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS3/CFT2. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

Revisit of renormalization of Einstein-Maxwell theory at one-loop

In a series of the recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the presence of the trace mode, with the 4D covariance. A subtlety in the background field method also requires careful handling. This status of the matter motivated us to revisit an Einstein-scalar system in one of the sequels. Continuing the endeavors, we revisit the one-loop renormalization of an Einstein-Maxwell system in the present work. The systematic renormalization of the cosmological and Newton’s constants is carried out by applying the refined background field method. One-loop beta function of the vector coupling constant is explicitly computed and compared with the literature. The longstanding problem of gauge choice-dependence of the effective action is addressed and the manner in which the gauge-choice independence is restored in the present framework is discussed. The formalism also sheds light on background independent analysis. The renormalization involves a metric field redefinition originally introduced by ‘t Hooft; with the field redefinition the theory should be predictive.