<p>We compute the parity-odd part of the Weyl anomaly for chiral fermions in a background gravitational field. We start from a manifestly real form of the Lagrangian (that is, not only real up to a total derivative), and we regularize it by means of Pauli-Villars fermions. All parity-odd terms in the anomaly cancel in the <i>integrand</i>, so that the result of the anomaly is necessarily parity even.</p>

Spain

Enrique Álvarez

CERN

Luis Álvarez-Gaumé

Jesús Anero

Carmelo P. Martín

Weyl anomaly for chiral fermions

The Kerr-Schild gauge is generalized to the case that the vector generating the deformation is not null. Contrary to naive expectations, this vector generates a finite expansion for the curvature tensor. We prove a theorem on the conditions for the deformed metric being Ricci flat, namely that the deformation vector must be irrotational (then geodesic) in the background spacetime.

Generalized Kerr-Schild gauge

Some aspects of quantum field theory in a general (i.e. non inertial) frame of Minkowski spacetime are studied. Conditions for the presence of horizons as well as for the modification of the definition of positive energy solutions are examined. The standard wisdom is confirmed that none of these phenomena is generic. This corroborates that in the general case there is no natural way to define positive frequencies, which is the standard road to define particles. In that sense, (as well as in others) non inertial frames are similar to curved spacetimes.

Some aspects of QFT in non-inertial frames

We analyze some aspects of the cubic action for gravity recently proposed by Cheung and Remmen, which is a particular instance of a first order (Palatini) action. In this approach both the spacetime metric and the connection are treated as independent fields. We discuss its BRST invariance and compute explicitly the one-loop contribution of quantum fluctuations around flat space, checking that the corresponding Slavnov-Taylor identities are fulfilled. Finally, our results on a first order action are compared with the existing ones corresponding to a second order action.

Carmelo Martin

One loop analysis of the cubic action for gravity

Generalized Kerr–Schild nilpotent deformations of an arbitrary background spacetime  $$\overline{g}_{\mu \nu }(x)$$  <math> <mrow> <msub> <mover> <mi>g</mi> <mo>¯</mo> </mover> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>   are considered. Those are of the form  $$\overline{g}_{\mu \nu }+l_\mu l_\nu $$  <math> <mrow> <msub> <mover> <mi>g</mi> <mo>¯</mo> </mover> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>l</mi> <mi>μ</mi> </msub> <msub> <mi>l</mi> <mi>ν</mi> </msub> </mrow> </math>   with  $$l^2=0$$  <math> <mrow> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mrow> </math>  . The relationship between the Ricci tensor of the background metric and the Ricci tensor of the deformed metric is found exactly. It consists of two terms, one is essentially the Fierz–Pauli operator, and the other is new. When the background is flat, the Kerr–Schild family is recovered. Novel examples for more general backgrounds (even including some simple sources) are discussed.

Some consequences of the Kerr–Schild gauge

Gravitational plane waves (when Ricci flat) belong to the VSI family. The achronym VSI stands for vanishing scalar invariants, meaning that all scalar invariants built out of Riemann tensor and its derivatives vanish, although the Riemann tensor itself does not. In the particular case of plane waves many interesting phenomena have been uncovered for strings propagating in this background. Here we comment on gravitons propagating in such a spacetime.

Irene Sánchez-Ruiz

Gravitons in a gravitational plane wave

It is well-known that in unimodular gravity (UG) the cosmological constant is not sourced by a constant energy density, but rather appears as some sort of integration constant. In this work we try to flesh this out by studying in some detail a couple of examples, one from cosmology and the other from gravitational collapse.

The origin of the cosmological constant in unimodular gravity

When implementing a nonlinear constraint in quantum field theory by means of a Lagrange multiplier, <math><mi>λ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, it is often the case that quantum dynamics induce quadratic and even higher-order terms in <math><mi>λ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, which then does not enforce the constraint anymore. This is illustrated in the case of unimodular gravity, where the constraint is that the metric tensor has to be unimodular (<math><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≡</mo><mi>det</mi><mtext> </mtext><msub><mrow><mi>g</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math>).

Carmelo P. Martin

Eduardo Velasco-Aja

Quantum dynamics of Lagrange multipliers

The maximally helicity violating tree-level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in the two theories.

Sergio González-Martín

Unimodular trees versus Einstein trees

A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.