Canonical pure spinor (Fermionic) T-duality

We establish that the recently discovered fermionic T-duality can be viewed as a canonical transformation in phase space. This requires a careful treatment of constrained Hamiltonian systems. Additionally, we show how the canonical transformation approach for bosonic T-duality can be extended to include Ramond--Ramond backgrounds in the pure spinor formalism.Comment: 14 page

Holographic renormalization as a canonical transformation

The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equations of motion that inherits a well defined symplectic form from that on phase space. The requirement of a well defined symplectic form is essential and often leads to a necessary repackaging of the degrees of freedom. (ii) Once the space of asymptotic solutions has been constructed in terms of the correct degrees of freedom, then there exists a boundary term that is obtained as a certain solution of the Hamilton-Jacobi equation which simultaneously makes the variational problem well defined and preserves the symplectic form. This procedure is identical to holographic renormalization in the case of asymptotically AdS gravity, but it is applicable to any Hamiltonian system.Comment: 37 pages; v2 minor corrections in section 2, 2 references and a footnote on Palatini gravity added. Version to appear in JHE

Poisson-Lie T-plurality as canonical transformation

We generalize the prescription realizing classical Poisson-Lie T-duality as canonical transformation to Poisson-Lie T-plurality. The key ingredient is the transformation of left-invariant fields under Poisson-Lie T-plurality. Explicit formulae realizing canonical transformation are presented and the preservation of canonical Poisson brackets and Hamiltonian density is shown.Comment: 11 pages. Details of calculations added, version accepted for publicatio

Smooth Bosonization as a Quantum Canonical Transformation

We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which smoothly interpolate between the massive Thirring model and the sine-Gordon model. This provides an implementation of smooth bosonization proposed by Damgaard et al. as well as an example of a quantum canonical transformation for a quantum field theory.Comment: 20 pages, revte

3d mirror symmetry as a canonical transformation

We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition functions are given by simple modifications of the argument of the Airy function found previously. With these extra parameters it is easy to see that mirror-symmetry corresponds to linear canonical transformations on the phase space (or operator algebra) of the 1-dimensional fermions.Comment: 11 pages, 2 figures. v2: figure added - version published in JHE

New forms of BRST symmetry in rigid rotor

We derive the different forms of BRST symmetry by using the Batalin-Fradkin-Vilkovisky formalism in a rigid rotor. The so called "dual-BRST" symmetry is obtained from usual BRST symmetry by making a canonical transformation in the ghost sector. On the other hand, a canonical transformation in the sector involving Lagrange multiplier and its corresponding momentum leads to a new form of BRST as well as dual-BRST symmetry.Comment: 10 Pages, revtex, No Fig