From instantons to AdS boundaries: tracing the geometric path from quantum anomalies to massive gravity.
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Date
2026
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Publisher
Universidad de Concepción
Abstract
This thesis presents two independent investigations of the role of symmetry, geometry, and boundary data in gravitational field theories. The first one concerns the axial anomaly of charged Dirac fermions on gravitational instantons coupled to nonlinear conformal electrodynamics. The second one, on the other hand, deals with extrinsic holographic renormalization of threedimensional New Massive Gravity. In the first part, we consider Einstein gravity coupled to ModMax electrodynamics: a nonlinear deformation of Maxwell theory that preserves classical conformal invariance and electromagnetic duality. We analyze nonlinearly charged Taub–NUT and Eguchi–Hanson configurations and evaluate the Dirac index using the Atiyah–Patodi–Singer theorem, including the spectral asymmetry of the boundary Dirac operator. The comparison identifies how the nonlinear gauge background fields modify the bulk and boundary contributions to the axial anomaly. In the Taub–NUT case, the result agrees with its Maxwell counterpart, whereas the Eguchi–Hanson configuration exhibits an explicit nonlinear dependence in the gauge-field contribution when expressed in terms of the solution parameters. In the second part, we construct extrinsic boundary counterterms for asymptotically anti-de Sitter solutions of New Massive Gravity. For the Brown-Henneaux boundary conditions, a term linear in the extrinsic curvature reproduces the finite boundary response obtained from the auxiliary-field formulation. At the degenerate point, however, the field equations allow for relaxed AdS boundary conditions an additional Fefferman–Graham coefficient is allowed, and a quadratic extrinsic boundary functional accommodates the weakened fall-offs. The variational principle, boundaryWard identities, and Noether–Wald charges are obtained, and their equivalence with previous methods is shown. Together, these studies demonstrate complementary ways in which global and asymptotic information enters the definition of quantum and gravitational observables.
Description
Tesis presentada para optar al grado de Doctor/a en Física.
Keywords
Gravitational fields