Francesco Toppan

Towards the quantization of the Green-Schwarz heterotic string

Abstract The quantization of the Green-Schwarz heterotic string is reviewed. An improved solution for the master equation is found. The problem of the quantization on a higher-genus Riemann surface is discussed, and a careful analysis of the cancellation of the conformal anomaly is presented.

b-c system approach to minimal models. The genus-zero case

Abstract We present a method based on real weight b−c system to study conformal minimal models. In particular it reproduces the results of the Coulomb gas approach, while shedding light on the topological origin of the charge at infinity.

Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum Mechanics

We prove that the invariance of the N = 2 superconformal quantum mechanics is controlled by subalgebras of a given twisted superalgebra made of 6 fermionic (nilpotent) generators and 6 bosonic generators (including a central charge). The superconformal quantum mechanics actions are invariant under subalgebras of this quite large twisted superalgebra. They are in fact fully determined by a subalgebra with only 2 fermionic and 2 bosonic (the central charge and the ghost number) generators. The invariant actions are Qi-exact, with a Qi′-exact (i ′ 6 i) antecedent for some of its 6 fermionic generators. It follows that the superconformal quantum mechanics actions with Calogero potentials are uniquely determined even if, in its bosonic sector, the twisted superalgebra does not contain the one-dimensional conformal algebra sl(2), but only its Borel subalgebra. The general coordinate covariance of the non-linear sigma-model for the N = 2 supersymmetric quantum mechanics in a curved target space is fully implied only by its worldline invariance under a pair of the 6 twisted supersymmetries. The transformation connecting the ordinary and twisted formulations of the N = 2 superconformal quantum mechanics is explicitly presented.

Chern-Simons AdS(5) supergravity in a Randall-Sundrum background

Abstract Chern–Simons AdS supergravity theories are gauge theories for the super-AdS group. These theories possess a fermionic symmetry which differs from standard supersymmetry. In this paper, we study five-dimensional Chern–Simons AdS supergravity in a Randall–Sundrum scenario with two Minkowski 3-branes. After making modifications to the D = 5 Chern–Simons AdS supergravity action and fermionic symmetry transformations, we obtain a Z 2 -invariant total action S = S ˜ bulk + S brane and fermionic transformations δ ˜ ϵ . While δ ˜ ϵ S ˜ bulk = 0 , the fermionic symmetry is broken by S brane . Our total action reduces to the original Randall–Sundrum model when S ˜ bulk is restricted to its gravitational sector. We solve the Killing spinor equations for a bosonic configuration with vanishing su ( N ) and u ( 1 ) gauge fields.

Chains of topological oscillators with instantons and calculable topological observables in topological quantum mechanics

We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.

Constrained Generalized Supersymmetries

We present a classification of admissible types of constraint (hermitian, holomorphic, with reality condition on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. A generalized supersymmetry algebra involving n‐component real spinors Qa is given by the anticommutators {Qa,Qb}u2009=u2009Zab where the matrix Z appearing in the r.h.s. is the most general symmetric matrix. A complex generalized supersymmetry algebra is expressed in terms of complex spinors Qa and their complex conjugate Q* ȧ. The most general (with a saturated r.h.s.) algebra is in this case given by {Qa,Qb}u2009=u2009Pab{Q*ȧ,u2009Q*ḃ}u2009=u2009P*ȧḃ{Qa,Q*ḃ}u2009=u2009Raḃ where the matrix Pab is symmetric, while Rab is hermitian. The bosonic right hand side can be expressed in terms of the rank‐k totally antisymmetric tensors Pabu2009=u2009Σk(CΓ[μ1u2009…μu2009k])abP[μ1u2009…μu2009k].The decomposition in terms of anti‐symmetric tensors for any space‐time up to dimension D = 13 is presented. Real type, complex type, and quaternionic type space‐times are class...