48 research outputs found
Global Seiberg-Witten maps for U(n)-bundles on tori and T-duality
Seiberg-Witten maps are a well-established method to locally construct
noncommutative gauge theories starting from commutative gauge theories. We
revisit and classify the ambiguities and the freedom in the definition.
Geometrically, Seiberg-Witten maps provide a quantization of bundles with
connections. We study the case of U(n)-vector bundles on two-dimensional tori,
prove the existence of globally defined Seiberg-Witten maps (induced from the
plane to the torus) and show their compatibility with Morita equivalence.Comment: 28 pages. Revised version: sharpened in Sec. 4.3 the study of the
Seiberg-Witten maps for sections in the adjoint, related to their ordering
ambiguities; added sum of connections for tensor product bundles in Sec. 5;
improved in Sec. 5.1 the compatibility between Seiberg-Witten map and
T-duality transformation
T-duality without isometry via extended gauge symmetries of 2D sigma models
Target space duality is one of the most profound properties of string theory.
However it customarily requires that the background fields satisfy certain
invariance conditions in order to perform it consistently; for instance the
vector fields along the directions that T-duality is performed have to generate
isometries. In the present paper we examine in detail the possibility to
perform T-duality along non-isometric directions. In particular, based on a
recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge
invariance for an extended set of gauge transformations imposes weaker
constraints than in the standard case, notably the corresponding vector fields
are not Killing. This formulation enables us to follow a procedure analogous to
the derivation of the Buscher rules and obtain two dual models, by integrating
out once the Lagrange multipliers and once the gauge fields. We show that this
construction indeed works in non-trivial cases by examining an explicit class
of examples based on step 2 nilmanifolds.Comment: 1+18 pages; version 2: corrections and improvements, more complete
version than the published on
Sigma-model limit of Yang-Mills instantons in higher dimensions
We consider the Hermitian Yang-Mills (instanton) equations for connections on
vector bundles over a 2n-dimensional K\"ahler manifold X which is a product Y x
Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that
in the adiabatic limit, when the metric in the Z direction is scaled down, the
gauge instanton equations on Y x Z become sigma-model instanton equations for
maps from Y to the moduli space M (target space) of gauge instantons on Z if
q>= 4. For q<4 we get maps from Y to the moduli space M of flat connections on
Z. Thus, the Yang-Mills instantons on Y x Z converge to sigma-model instantons
on Y while Z shrinks to a point. Put differently, for small volume of Z,
sigma-model instantons on Y with target space M approximate Yang-Mills
instantons on Y x Z.Comment: 1+14 pages; v2: 2 footnotes and 3 refs. added, published version; v3:
gauge-fixing on 3-torus corrected, 4 more refs. adde
Extended Riemannian Geometry II: Local Heterotic Double Field Theory
We continue our exploration of local Double Field Theory (DFT) in terms of
symplectic graded manifolds carrying compatible derivations and study the case
of heterotic DFT. We start by developing in detail the differential graded
manifold that captures heterotic Generalized Geometry which leads to new
observations on the generalized metric and its twists. We then give a
symplectic pre-NQ-manifold that captures the symmetries and the geometry of
local heterotic DFT. We derive a weakened form of the section condition, which
arises algebraically from consistency of the symmetry Lie 2-algebra and its
action on extended tensors. We also give appropriate notions of twists-which
are required for global formulations-and of the torsion and Riemann tensors.
Finally, we show how the observed -corrections are interpreted
naturally in our framework.Comment: v2: 30 pages, few more details added, typos fixed, published versio
Palatini-Lovelock-Cartan Gravity - Bianchi Identities for Stringy Fluxes
A Palatini-type action for Einstein and Gauss-Bonnet gravity with non-trivial
torsion is proposed. Three-form flux is incorporated via a deformation of the
Riemann tensor, and consistency of the Palatini variational principle requires
the flux to be covariantly constant and to satisfy a Jacobi identity. Studying
gravity actions of third order in the curvature leads to a conjecture about
general Palatini-Lovelock-Cartan gravity. We point out potential relations to
string-theoretic Bianchi identities and, using the Schouten-Nijenhuis bracket,
derive a set of Bianchi identities for the non-geometric Q- and R-fluxes which
include derivative and curvature terms. Finally, the problem of relating
torsional gravity to higher-order corrections of the bosonic string-effective
action is revisited.Comment: 25 pages, notation improved, refs adde
Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
In this paper we study the general conditions that have to be met for a
gauged extension of a two-dimensional bosonic sigma-model to exist. In an
inversion of the usual approach of identifying a global symmetry and then
promoting it to a local one, we focus directly on the gauge symmetries of the
theory. This allows for action functionals which are gauge invariant for rather
general background fields in the sense that their invariance conditions are
milder than the usual case. In particular, the vector fields that control the
gauging need not be Killing. The relaxation of isometry for the background
fields is controlled by two connections on a Lie algebroid L in which the gauge
fields take values, in a generalization of the common Lie-algebraic picture.
Here we show that these connections can always be determined when L is a Dirac
structure in the H-twisted Courant algebroid. This also leads us to a
derivation of the general form for the gauge symmetries of a wide class of
two-dimensional topological field theories called Dirac sigma-models, which
interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term
twisted) Poisson sigma model.Comment: 1+27 pages; version 2: minor correction in the introduction; version
3: minor corrections to match published version, references updated,
acknowledgement adde