Related papers: Homotopy RG Flow and the Non-Linear $\sigma$-model
We introduce a two-dimensional sigma model associated with a Jacobi manifold. The model is a generalisation of a Poisson sigma model providing a topological open string theory. In the Hamiltonian approach first class constraints are…
Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with…
Kapustin and Witten showed that a twisted version of N=4 gauge theory in four dimensions compactifies to a two-dimensional sigma-model whose target space is the Hitchin moduli space. In this talk, I consider the reduction of the gauge…
The scattering amplitudes of gauge bosons in heterotic and open superstring theories are related by the single-valued projection which yields heterotic amplitudes by selecting a subset of multiple zeta value coefficients in the $\alpha'$…
We study non-linear sigma models on target manifolds with constant (positive or negative) curvature using the functional renormalization group and the background field method. We pay particular attention to the splitting Ward identities…
We define a sigma model with doubled target space and calculate its background field equations. These coincide with generalised metric equation of motion of double field theory, thus the double field theory is the effective field theory for…
We construct the holographic renormalization group (RG) flow of thermo-electric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain…
We introduce some new curvature quantities such as conformal Ricci curvature and bi-Ricci curvature and extend the classical Myers theorem under these new curvature conditions. Moreover, we are able to obtain the Myers type theorem for…
In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic…
Holographic RG flows are studied in an Einstein-dilaton theory with a general potential. The superpotential formalism is utilized in order to characterize and classify all solutions that are associated to asymptotically AdS space-times.…
Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci operator of an oriented closed Riemannian manifold can be…
We review the main aspects of Ricci flows as they arise in physics and mathematics. In field theory they describe the renormalization group equations of the target space metric of two dimensional sigma models to lowest order in the…
We review recent results relating linear stability to dynamical stability and the scalar curvature rigidity of Einstein manifolds. We discuss closed and open Einstein manifolds as well as complete noncompact Einstein manifolds which are…
We show that strong subadditivity provides a simple derivation of the $g$-theorem for the boundary renormalization group flow in two-dimensional conformal field theories. We work out its holographic interpretation and also give a derivation…
We use geometric arguments to derive a possible form for the radial part of the ``zero-mode Hamiltonian'' for the two dimensional sigma model with target space S^3, or more generally a compact simply connected Lie group.
The properties of the effective sigma-model for D-dimensional Einstein gravity based on multidimensional geometries is analyzed. Besides pure geometry, additional minimally coupled scalars and (p+2)-forms are considered which yield an…
It is known that the $U(2)$ Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. While it is decomposed into the $SU(2)$ Wess-Zumino-Witten model and a free compact boson, the former is…
We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear…
Using field-theoretic techniques, we study the $SU(3)$ analogue of anti-ferromagnetic Heisenberg spin model on the triangular lattice putting the $p$-box symmetric representation on each site. Taking the large-$p$ limit, we show that the…
In this letter, cosmology of a simple NMDC gravity with $\xi R \phi_{,\mu}\phi^{,\mu}$ term and a free kinetic term is considered in flat geometry and in presence of dust matter. A logarithm field transformation $\phi' = \mu \ln \phi$ is…