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We study the renormalizability of quantum gravity near two dimensions. Our formalism starts with the tree action which is invariant under the volume preserving diffeomorphism. We identify the BRS invariance which originates from the full…

We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…

We provide an elementary systematic discussion of single-trace matrix actions and of the group of matrix reparameterization that acts on them. The action of this group yields a generalized notion of gauge invariance which encompasses…

We show that vanishing of the sigma-model beta-functions for the metric $g_{\mu\nu}$, antisymmetric tensor $B_{\mu\nu}$ and dilaton $\Phi$ of any string-theory model in $D$ dimensions at tree level can be obtained from a universal effective…

We consider the N=2 supersymmetric Born-Infeld action and compute one-loop divergences quantizing the theory in N=1 superspace. We find that in the presence of non constant curvature the theory is not renormalizable. The structure of the…

In this paper we study long distance modifications of gravity obtained by considering actions that are singular in the limit of vanishing curvature. In particular, we showed in a previous publication that models that include inverse powers…

In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We…

We consider analogs of Yang-Mills theories for non-semisimple real Lie algebras which admit invariant non-degenerate metrics. These 4-dimensional theories have many similarities with corresponding WZW models in 2 dimensions and Chern-Simons…

We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where…

We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the $\alpha '$ expansion of the heterotic string low energy effective theory. The generalized tangent space and…

We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…

Since fields in the heavy quark effective theory are described by both a velocity and a residual momentum, there is redundancy in the theory: small shifts in velocity may be absorbed into a redefinition of the residual momentum. We…

There exists a widely spread notion that gravitational effects can strongly violate global symmetries. It may lead to many important consequences. We will argue, in particular, that nonperturbative gravitational effects in the axion theory…

In commutative invariant theory, a classical result due to Auslander says that if $R = \Bbbk[x_1, \dots, x_n]$ and $G$ is a finite subgroup of $\text{Aut}_{\text{gr}}(R) \cong \text{GL}(n,\Bbbk)$ which contains no reflections, then there is…

We consider effects of symmetries on renormalization properties of the collinear effective theory. We investigate which types of operators are possible in the effective theory satisfying gauge invariance, reparameterization invariance and…

The corrections to the tree-level effective action for the bosonic string up to second order in $\alpha'$ are fixed by requiring its dimensional reduction to $26-d$ dimensions to be compatible with $O(d,d)$ symmetry. The result is in…

Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries are…

Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar…

It has been recently observed that the imposition of the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order $\alpha'^2$, up to an…

Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…