55 research outputs found
-algebras and membrane sigma models
Membrane sigma-models have been used for the systematic description of closed
strings in non-geometric flux backgrounds. In particular, the conditions for
gauge invariance of the corresponding action functionals were related to the
Bianchi identities for the fluxes. In this contribution we demonstrate how to
express these Bianchi identities in terms of homotopy relations of the
underlying -algebra for the case of the Courant sigma-model. We argue
that this result can be utilized in understanding the constraint structure of
Double Field Theory and the corresponding membrane sigma-model.Comment: 13 pages; contribution to the proceedings of the Humboldt Kolleg
Frontiers in Physics: From the Electroweak to the Planck Scales, 15 - 19
September 2019, Corfu, Greec
Dirac structures on nilmanifolds and coexistence of fluxes
We study some aspects of the generalized geometry of nilmanifolds and examine
to which extent different types of fluxes can coexist on them. Nilmanifolds
constitute a class of homogeneous spaces which are interesting in string
compactifications with fluxes since they carry geometric flux by construction.
They are generalized Calabi-Yau spaces and therefore simple examples of
generalized geometry at work. We identify and classify Dirac structures on
nilmanifolds, which are maximally isotropic subbundles closed under the Courant
bracket. In the presence of non-vanishing fluxes, these structures are twisted
and closed under appropriate extensions of the Courant bracket. Twisted Dirac
structures on a nilmanifold may carry multiple coexistent fluxes of any type.
We also show how dual Dirac structures combine to Courant algebroids and work
out an explicit example where all types of generalized fluxes coexist. These
results may be useful in the context of general flux compactifications in
string theory.Comment: 1+25 pages; v2: clarifying comments and 6 references added, published
versio
Sigma models for genuinely non-geometric backgrounds
The existence of genuinely non-geometric backgrounds, i.e. ones without
geometric dual, is an important question in string theory. In this paper we
examine this question from a sigma model perspective. First we construct a
particular class of Courant algebroids as protobialgebroids with all types of
geometric and non-geometric fluxes. For such structures we apply the
mathematical result that any Courant algebroid gives rise to a 3D topological
sigma model of the AKSZ type and we discuss the corresponding 2D field
theories. It is found that these models are always geometric, even when both
2-form and 2-vector fields are neither vanishing nor inverse of one another.
Taking a further step, we suggest an extended class of 3D sigma models, whose
world volume is embedded in phase space, which allow for genuinely
non-geometric backgrounds. Adopting the doubled formalism such models can be
related to double field theory, albeit from a world sheet perspective.Comment: 1+34 pages, v2. added references and additional comments; published
versio
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
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
Gauging as constraining: the universal generalised geometry action in two dimensions
One of the central concepts in modern theoretical physics, gauge symmetry, is
typically realised by lifting a finite-dimensional global symmetry group of a
given functional to an infinite-dimensional local one by extending the
functional to include gauge fields. In this contribution we review the
construction of gauged actions for two-dimensional sigma models, considering a
more general notion to be gauged, namely that of a (possibly singular)
foliation. In particular, the original action does not need to have any global
symmetry for this purpose. Moreover, reformulating the ungauged theory by means
of auxiliary 1-form fields taking values in the generalised tangent bundle over
the target, all possible such gauge theories result from restriction of these
fields to take values in (possibly small) Dirac structures. This turns all the
remaining 1-form fields into gauge fields and leads to the presence of a local
symmetry. We recall all needed mathematical notions, those of (higher) Lie
algebroids, Courant algebroids, and Dirac structures.Comment: 20 pages; proceedings of "Recent Developments in Strings and
Gravity", Corfu Summer Institute 201
Basic curvature and the Atiyah cocycle in gauge theory
We study connections on higher structures such as Lie and Courant algebroids
and their description as differential graded manifolds and explore the role of
their basic curvature tensor and of the Atiyah cocycle in topological sigma
models and higher gauge theories. The basic curvature of a connection on a Lie
algebroid is a measure for the compatibility of the connection with the Lie
bracket and it appears in the BV operator of topological sigma models in 2D.
Here we define a basic curvature tensor for connections on Courant algebroids
and we show that in the description of a Courant algebroid as a QP manifold it
appears naturally as part of the homological vector field together with the
Gualtieri torsion of a generalised connection. The Atiyah cocycle of a
connection on a differential graded manifold is a measure of the compatibility
of the connection with the homological vector field. We argue that in the
graded-geometric description of higher gauge theories, the structure of gauge
transformations is governed by a Kapranov L algebra, whose binary
bracket is given by the Atiyah cocycle. We also revisit some aspects of derived
structures and we uncover the role of the Atiyah cocycle in deriving
-tensors for -connections on Lie and Courant algebroids from ordinary
tensors on differential graded manifolds.Comment: 64 page
Dynamical and Quenched Random Matrices and Homolumo Gap
We consider a rather general type of matrix model, where the matrix M
represents a Hamiltonian of the interaction of a bosonic system with a single
fermion. The fluctuations of the matrix are partly given by some fundamental
randomness and partly dynamically, even quantum mechanically. We then study the
homolumo-gap effect, which means that we study how the level density for the
single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In
the case of the quenched randomness (the fundamental one) dominating the
quantum mechanical one we show that in the first approximation the homolumo gap
is characterized by the absence of single-fermion levels between two steep gap
boundaries. The filled and empty level densities are in this first
approximation just pushed, each to its side. In the next approximation these
steep drops in the spectral density are smeared out to have an error-function
shape. The studied model could be considered as a first step towards the more
general case of considering a whole field of matrices - defined say on some
phase space - rather than a single matrix.Comment: 15 pages, 2 figures; v2. substantial improvements, published in IJMP
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