74 research outputs found
Review of localization for 5d supersymmetric gauge theories
We give a pedagogical review of the localization of supersymmetric gauge
theory on 5d toric Sasaki-Einstein manifolds. We construct the cohomological
complex resulting from supersymmetry and consider its natural toric
deformations with all equivariant parameters turned on. We also give detailed
discussion on how the Sasaki-Einstein geometry permeates every aspect of the
calculation, from Killing spinor, vanishing theorems to the index theorems.Comment: This is a contribution to the review volume `Localization techniques
in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17
Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be
downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or
http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pd
Observables in the equivariant A-model
We discuss observables of an equivariant extension of the A-model in the
framework of the AKSZ construction. We introduce the A-model observables, a
class of observables that are homotopically equivalent to the canonical AKSZ
observables but are better behaved in the gauge fixing. We discuss them for two
different choices of gauge fixing: the first one is conjectured to compute the
correlators of the A-model with target the Marsden-Weinstein reduced space; in
the second one we recover the topological Yang-Mills action coupled with
A-model so that the A-model observables are closed under supersymmetry.Comment: 16 pages; minor correction
2D and 3D topological field theories for generalized complex geometry
Using the Alexandrov–Kontsevich–Schwarz–Zaboronsky (AKSZ) prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of as 2D and 3D generalizations of A- and B-models. Within the BV framework we show that the 3D model on a two-manifold cross an interval can be reduced to the 2D model
Courant-like brackets and loop spaces
We study the algebra of local functionals equipped with a Poisson bracket. We
discuss the underlying algebraic structures related to a version of the
Courant-Dorfman algebra. As a main illustration, we consider the functionals
over the cotangent bundle of the superloop space over a smooth manifold. We
present a number of examples of the Courant-like brackets arising from this
analysis.Comment: 20 pages, the version published in JHE
Topological twisted sigma model with H-flux revisited
In this paper we revisit the topological twisted sigma model with H-flux. We
explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian
geometry. we show that the resulting action consists of a BRST exact term and
pullback terms, which only depend on one of the two generalized complex
structures and the B-field. We then discuss the topological feature of the
model.Comment: 16 pages. Appendix adde
T-duality for the sigma model with boundaries
We derive the most general local boundary conditions necessary for T-duality
to be compatible with superconformal invariance of the two-dimensional N=1
supersymmetric nonlinear sigma model with boundaries. To this end, we construct
a consistent gauge invariant parent action by gauging a U(1) isometry, with and
without boundary interactions. We investigate the behaviour of the boundary
conditions under T-duality, and interpret the results in terms of D-branes.Comment: 48 pages, LaTeX, v2: typos corrected, references adde
Euclidean Supersymmetry, Twisting and Topological Sigma Models
We discuss two dimensional N-extended supersymmetry in Euclidean signature
and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that
only an A-twist is possible. To formulate a B-twist, or to construct Euclidean
N=2 models with H-flux so that the target geometry is generalised Kahler, it is
necessary to work with a complexification of the sigma models. These issues are
related to the obstructions to the existence of non-trivial twisted chiral
superfields in Euclidean superspace.Comment: 8 page
Linearizing Generalized Kahler Geometry
The geometry of the target space of an N=(2,2) supersymmetry sigma-model
carries a generalized Kahler structure. There always exists a real function,
the generalized Kahler potential K, that encodes all the relevant local
differential geometry data: the metric, the B-field, etc. Generically this data
is given by nonlinear functions of the second derivatives of K. We show that,
at least locally, the nonlinearity on any generalized Kahler manifold can be
explained as arising from a quotient of a space without this nonlinearity.Comment: 31 pages, some geometrical aspects clarified, typos correcte
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