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In contrast to Hamiltonian perturbation theory which changes the time evolution, "spacelike deformations" proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of…
We introduce a precise notion, in terms of few Schlessinger's type conditions, of extended deformation functors which is compatible with most of recent ideas in the Derived Deformation Theory (DDT) program and with geometric examples. With…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
The unimodular version of the ghost-free higher derivative gravity is obtained. It is the unimodular reduction of some particular lagrangians quadratic in curvature.
We consider Higher-Order Scalar-Tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We provide a full classification of theories that…
Recent progress seems to suggest that one must modify General Relativity (GR) to stably violate the null energy condition and avoid the cosmological singularity. However, with the higher-order derivative operators of scalar field (a…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
In this paper we construct a class of Degenerate Higher-Order Scalar-Tensor (DHOST) theories with an extra scalar field, which admits viable solutions of bouncing universe satisfying the following requirements: (i) absence of…
A generalized twistor transform for spinning particles in 3+1 dimensions is constructed that beautifully unifies many types of spinning systems by mapping them to the same twistor, thus predicting an infinite set of duality relations among…
A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…
In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which…
This contribution reviews scalar-tensor theories whose Lagrangian contains second-order derivatives of a scalar field but nevertheless propagate only one scalar mode (in addition to the usual two tensor modes), and are thus not plagued with…
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically…
We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can…
Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…
We consider high-derivative equations obtained setting to zero the divergence of the higher-spin curvatures in metric-like form, showing their equivalence to the second-order equations emerging from the tensionless limit of open string…
Degenerate scalar-tensor theories are recently proposed covariant theories of gravity coupled with a scalar field. Despite being characterised by higher order equations of motion, they do not propagate more than three degrees of freedom,…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
We introduce and study generalized holographic superconductors with higher derivative couplings between the field strength tensor and a complex scalar field, in four dimensional AdS black hole backgrounds. We study this theory in the probe…
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…