Mirian Tsulaia

We develop the (super)twistor approach to D0-brane, which is the massive type IIA superparticle in ten-dimensional spacetime. The basic variables are hexadecuplet of constrained O S p ( 32 | 1 ) supertwistors similar but not identical to the ones which have been used for the description of 11D massless superparticle, also known as M0-brane. We show how the constrained supertwistor formulation is related to the spinor moving frame approach to D0-brane. We perform the quantization of the model by two different methods and discuss the relation of the results with the quantization of the spinor moving frame formulation of D0-branes. The quantum state spectrum describes the massive counterpart of the linearized type IIA supergravity.

A bstract: We develop a systematic approach to the computation of gauge invariant quartic interactions between reducible massive and massless higher spin fields. Extending the BRST formulation of existing cubic results, we obtain a single constraint for each off-shell quartic vertex that ensures both the gauge invariance of the Lagrangian and formal closure of the gauge algebra at quartic order. A solution to these equations is presented. The general equation is then reduced to an on-shell version to reduce complexity. We find example solutions for the off-shell and on-shell quartic vertices in low spin examples relevant to the problem of black hole scattering.

A bstract: We quantize D0-brane, the simplest representative of the family of supersymmetric Dirichlet p -branes, in its spinor moving frame formulation and analyze its quantum state spectrum. Besides being a preparatory stage for quantization of the complete supersymmetric multiple D0-brane (mD0) model, which is presently known only in the frame of spinor moving frame formalism, this is interesting as its own: despite the covariant quantization of D = 10 D0-brane was discussed before, its quantum state spectrum was not analyzed and its field theory, describing that, was not studied. We show that the quantum state vector of the D0-brane is described by an on-shell superfield that collects the fields of the massive counterpart of the linearized type IIA supergravity supermultiplet which can be obtained as massive Kaluza-Klein mode of the dimensional reduction of the eleven dimensional supergravity down to ten dimensions. In conclusion, we briefly discuss a spinor helicity formalism for D0-brane which can be used as one of the basic elements for developing type IIA string theory amplitude calculus based on multiparticle generalizations of the on-shell superfields.

We give a brief introduction into the gauge invariant formulation of irreducible massive bosonic higher spin fields. We discuss both free Lagrangians and the ones which include cubic interactions. We demonstrate an application of these Lagrangians to a description of the interactions between Kerr black holes in a Post Minkowskian approximation.

We consider N = 1 supersymmetric systems in d = 4, 6 and 10 dimensions which consist of reducible bosonic and fermionic massless representations of the Poincaré group. We show in detail how to decompose the corresponding Lagrangians into a sum of Lagrangians for irreducible representations of the Poincaré group. We also outline a modification of this procedure in the case of an anti-de Sitter background.

Scattering of two Kerr Black Holes emitting gravitational waves can be captured by an effective theory of a massive higher-spin field interacting with the gravitational field. While other compact objects should activate a multitude of non-minimal interactions it is the black holes that should be captured by the simplest minimal interaction. Implementing massive higher-spin symmetry via a string-inspired BRST approach we construct an action that reproduces the correct cubic amplitude of Arkani-Hamed-Huang-Huang. The same is achieved for the root-Kerr theory, i.e. for the minimal electromagnetic interaction of a massive higher-spin field.

We study quantum properties of supersymmetric N=1 and N=4 extensions of the four dimensional bosonic Chiral Higher Spin Gravities (HiSGRAs). We discuss the spectra, the classical actions and define the Feynman rules in N=1 and N=4 superspaces in the light-front gauge. Using these Feynman rules, we compute tree and one-loop amplitudes for these systems. A dimensional reduction to a system with N=2 supersymmetry and with massive higher spin fields is performed and quantum properties of this system are discussed.

Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that the energy spectra and wavefunctions for discretized Quantum Mechanical systems can be found using the technique of N=2 Supersymmetric Quantum Mechanics exactly the same way as it is done for their continuous counterparts. As a demonstration of the present method, we find the energy spectrum for a discretized Coulomb potential and its ground state wave function.

We demonstrate how to reconstruct standard cubic vertices for N=1 supersymmetric Yang-Mills and Supergravities using various techniques adopted for the description of cubic interactions between higher spin fields.