18,424 research outputs found
First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-form
We show that in analogy to the introduction of Poisson structures twisted by
a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional
sigma models with Wess-Zumino term leads in a likewise way to twisting of
Courant algebroid structures by closed 4-forms H.
The presentation is kept pedagogical and accessible to physicists as well as
to mathematicians, explaining in detail in particular the interplay of field
transformations in a sigma model with the type of geometrical structures
induced on a target. In fact, as we also show, even if one does not know the
mathematical concept of a Courant algebroid, the study of a rather general
class of 3-dimensional sigma models leads one to that notion by itself.
Courant algebroids became of relevance for mathematical physics lately from
several perspectives - like for example by means of using generalized complex
structures in String Theory. One may expect that their twisting by the
curvature H of some 3-form Ramond-Ramond gauge field will become of relevance
as well.Comment: 25 pages, invited contribution to the Wolfgang Kummer memorial volum
Non-geometric String Backgrounds and Worldsheet Algebras
Using worldsheet Hamiltonian methods we derive a charge algebra which
generalizes the Courant bracket to include fluxes of general index type. This
is achieved by coupling a bi-vector to the Hamiltonian of the Polyakov model.
This bracket is useful to describe so-called non-geometric backgrounds and has
been discussed in the mathematics literature by Dmitry Roytenberg.Comment: 18 page
Hidden isometry of "T-duality without isometry"
We study the T-dualisability criteria of Chatzistavrakidis, Deser and Jonke
[3] who recently used Lie algebroid gauge theories to obtain sigma models
exhibiting a "T-duality without isometry". We point out that those
T-dualisability criteria are not written invariantly in [3] and depend on the
choice of the algebroid framing. We then show that there always exists an
isometric framing for which the Lie algebroid gauging boils down to standard
Yang-Mills gauging. The "T-duality without isometry" of Chatzistavrakidis,
Deser and Jonke is therefore nothing but traditional isometric non-Abelian
T-duality in disguise.Comment: 15 page
Geometry of Centroaffine Surfaces in
We use Cartan's method of moving frames to compute a complete set of local
invariants for nondegenerate, 2-dimensional centroaffine surfaces in
with nondegenerate centroaffine metric. We then
give a complete classification of all homogeneous centroaffine surfaces in this
class
Tachyon Condensates and String Theoretic Inflation
Cosmological solutions of the beta function equations for the background
fields of the closed bosonic string are investigated at the one-loop level.
Following recent work of Kostelecky and Perry, it is assumed that the spatial
sections of the space-time are conformally flat. Working in the sigma-model
frame, the non-trivial tachyon potential is utilized to determine solutions
with sufficient inflation to solve the smoothness and flatness problems. The
graceful exit and density perturbation constraints can also be successfully
implemented.Comment: FERMI-PUB 93/074-T, harvmac, 16 page
Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
We construct the solution of type IIB supergravity describing the integrable
lambda-deformation of the AdS_3 x S^3 supercoset. While the geometry
corresponding to the deformation of the bosonic coset has been found in the
past, our background is more natural for studying superstrings, and several
interesting features distinguish our solution from its bosonic counterpart. We
also report progress towards constructing the lambda-deformation of the AdS_5 x
S^5 supercoset.Comment: 31 pages, v2: references adde
Derivation of Einstein Cartan theory from general relativity
This work derives the elements of classical Einstein Cartan theory (EC) from
classical general relativity (GR) in two ways. (I) Derive translational
holonomy and the spin torsion field equation of EC for one Kerr mass in GR.
(II) Derive the field equations of EC as the continuum limit of a sequence of
discrete distributions of Kerr masses in classical GR with no electric charge.
his derivation does not extend to the quantum domain because of inequality
constraints. The convergence computations employ epsilon delta arguments, and
are not as rigorous as weak convergence in Sobolev norm. Derivation of EC from
GR strengthens the case for new physics derived from EC, including modeling
exchange of intrinsic and orbital angular momentum, removing some gravitational
singularities from Big Bang and black hole models, introducing a spin contact
force that is a geometric candidate for the origin of cosmic inflation, and
providing a better classical limit for theories of quantum gravity.Comment: 47 pages, 1 table, 66 equations, 3 figures, 93 lines of computer
algebra, 33 references. This version improves organization and many sections.
It argues that deriving EC from GR greatly strengthens the case for new
physics that is derived from EC; the new physics is listed. Section 2 updates
the 1986 paper below. Petti RJ, 1986, Gen Rel Grav vol 18, 441-46
Pseudoduality in Sigma Models
We revisit classical "on shell" duality, i.e., pseudoduality, in two
dimensional conformally invariant classical sigma models and find some new
interesting results. We show that any two sigma models that are "on shell"
duals have opposite 1-loop renormalization group beta functions because of the
integrability conditions for the pseudoduality transformation. A new result
states for any two compact Lie groups of the same dimension there is a natural
pseudoduality transformation that maps classical solutions of the WZW model on
the first group into solutions of the WZW model on the second group. This
transformation preserves the stress-energy tensor. The two groups can be
non-isomorphic such as B_n and C_n in the Cartan notation. This transformation
can be used for a new construction of non-local conserved currents. The new
non-local currents on G depend on the choice of dual group G-tilde.Comment: 28 pages, LaTeX fil
Elliptic solutions of generalized Brans-Dicke gravity with a non-universal coupling
We study a model of the generalized Brans-Dicke gravity presented in both the
Jordan and in the Einstein frames, which are conformally related. We show that
the scalar field equations in the Einstein frame are reduced to the geodesics
equations on the target space of the nonlinear sigma-model. The analytical
solutions in elliptical functions are obtained when the conformal couplings are
given by reciprocal exponential functions. The behavior of the scale factor in
the Jordan frame is studied using numerical computations. For certain
parameters the solutions can describe an accelerated expansion. We also derive
an analytical approximation in exponential functions.Comment: 24 pages, 3 figures; v2: typos fixed, few remarks and references
added; version to appear in EPJ
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