Superstring theoryをめぐって(放談室)

Three dimensional Einstein gravity with negative cosmological constant ?1/?2 deformed by a gravitational Chern-Simons action with coefficient 1/? is studied in an asymptotically AdS3 spacetime. It is argued to violate unitary or positivity for generic ? due to negative-energy massive gravitons. However at the critical value ?? = 1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by ?M = J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (cL,?cR) = (0,?3?/G).

https://iopscience.iop.org/article/10.1088/1126-6708/2008/04/082/pdf

Chiral gravity in three dimensions

We discuss mirror symmetry in generalized Calabi-Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi-Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU(3) structure and are termed half-flat; they are neither complex nor Ricci-flat and their holonomy group is no longer SU(3). We show that type IIA appropriately compactified on such manifolds gives the correct mirror-symmetric low-energy effective action.

Mirror Symmetry in Generalized Calabi-Yau Compactifications

Mirror symmetry in generalized Calabi–Yau compactifications ☆

String Lessons for Higher-Spin Interactions

A path-integral quantization method is proposed for dynamical systems whose clas- sical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the La- grangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d + 1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quan- tized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quanti- zation scheme is exemplified by several models including the ones whose classical dynamics are not variational.

Lagrange structure and quantization

We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. For all these models, the positive integrals of motion are explicitly constructed and the interactions are included such that they keep the system stable.

/pdf/classical-and-quantum-stability-of-higher-derivative-1jygvbd11o.pdf

Classical and quantum stability of higher-derivative dynamics

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.

BRST theory without Hamiltonian and Lagrangian

Poisson geometry of sigma models with extended supersymmetry

The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond $d=4.$ For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.

Simon L. Lyakhovich

Papers

Lagrange structure and quantization

Classical and quantum stability of higher-derivative dynamics

BRST theory without Hamiltonian and Lagrangian

Poisson geometry of sigma models with extended supersymmetry

Radiation reaction and renormalization in classical electrodynamics of a point particle in any dimension