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## Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory

Bochicchio, Marco
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.1%
We localize the loop equation of large-N YM theory in the ASD variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the ASD integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative ASD vortices of the EK reduction. An exact canonical beta function of NSVZ type that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.; Comment: 52 pages...

## Weak solutions of the cohomological equation on R^2 for regular vector fields

De Leo, Roberto
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.56%
In a recent article, we studied the global solvability of the so-called cohomological equation L_X f=g in C^\infty(\Rt), where X is a regular vector field on the plane and L_X the corresponding Lie derivative. In a joint article with T. Gramchev and A. Kirilov, we studied the existence of global L^1_{loc} weak solutions of the cohomological equation for vector fields depending only on one coordinate. Here we generalize the results of both articles by providing explicit conditions for the existence of global weak solutions to the cohomological equation when X is intrinsically Hamiltonian or of finite type.; Comment: 22 pages, 6 figures

## Cohomological equation and cocycle rigidity of parabolic actions in $SL(n,\RR)$

Wang, Zhenqi Jenny
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.6%
For any unitary representation $(\pi,\mathcal{H})$ of $G=SL(n,\RR)$, $n\geq 3$ without non-trivial $G$-invariant vectors, we study smooth solutions of the cohomological equation $\mathfrak{u}f=g$ where $\mathfrak{u}$ is a vector in the root space of $\mathfrak{sl}(n,\RR)$ and $g$ is a given vector in $\mathcal{H}$. We characterize the obstructions to solving the cohomological equation, construct smooth solutions of the cohomological equation and obtain tame Sobolev estimates for $f$. We also study common solutions to (the infinitesimal version of) the cocycle equation $\mathfrak{u}h=\mathfrak{v}g$, where $\mathfrak{u}$ and $\mathfrak{v}$ are commutative vectors in different root spaces of $\mathfrak{sl}(n,\RR)$ and $g$ and $h$ are given vectors in $\mathcal{H}$. We give precisely the condition under which the cocycle equation has common solutions: $(*)$ if $\mathfrak{u}$ and $\mathfrak{v}$ embed in $\mathfrak{sl}(2,\RR)\times \RR$, then the common solution exists. Otherwise, we show counter examples in each $SL(n,\RR)$, $n\geq 3$. As an application, we obtain smooth cocycle rigidity for higher rank parabolic actions over $SL(n,\RR)/\Gamma$, $n\geq 4$ if the Lie algebra of the acting parabolic subgroup contains a pair $\mathfrak{u}$ and $\mathfrak{v}$ satisfying property $(*)$ and prove that the cocycle rigidity fails otherwise. Especially...

## On the cohomological equation for interval exchange maps

Marmi, Stefano; Moussa, Pierre; Yoccoz, Jean-Christophe
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.45%
We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of Roth type'' imposed to an acceleration of the Rauzy--Veech--Zorich continued fraction expansion associated to T. Contents 0. French abridged version 1. Interval exchange maps and the cohomological equation. Main Theorem 2. Rauzy--Veech--Zorich continued fraction algorithm and its acceleration 3. Special Birkhoff sums 4. The Diophantine condition 5. Sketch of the proof of the theorem; Comment: 11 pages, french abstract and abridged version

## On the cohomological equation of magnetic flows

Dairbekov, Nurlan S.; Paternain, Gabriel P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.27%
We consider a magnetic flow without conjugate points on a closed manifold $M$ with generating vector field $\G$. Let $h\in C^{\infty}(M)$ and let $\theta$ be a smooth 1-form on $M$. We show that the cohomological equation $\G(u)=h\circ \pi+\theta$ has a solution $u\in C^{\infty}(SM)$ only if $h=0$ and $\theta$ is closed. This result was proved in \cite{DP2} under the assumption that the flow of $\G$ is Anosov.

## Asymptotics for the wave equation on differential forms on Kerr-de Sitter space

Hintz, Peter; Vasy, Andras
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.16%
We study asymptotics for solutions of Maxwell's equations, in fact of the Hodge-de Rham equation $(d+\delta)u=0$ without restriction on the form degree, on a geometric class of stationary spacetimes with a warped product type structure (without any symmetry assumptions), which in particular include Schwarzschild-de Sitter spaces of all spacetime dimensions $n\geq 4$. We prove that solutions decay exponentially to $0$ or to stationary states in every form degree, and give an interpretation of the stationary states in terms of cohomological information of the spacetime. We also study the wave equation on differential forms and in particular prove analogous results on Schwarzschild-de Sitter spacetimes. We demonstrate the stability of our analysis and deduce asymptotics and decay for solutions of Maxwell's equations, the Hodge-de Rham equation and the wave equation on differential forms on Kerr-de Sitter spacetimes with small angular momentum.; Comment: 43 pages

## Cohomological construction of relative twists

Toledano-Laredo, V.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.15%
Let g be a complex, semi-simple Lie algebra, h a Cartan subalgebra of g and D a subdiagram of the Dynkin diagram of g. Let g_D and l_D be the corresponding semi-simple and Levi subalgebras and consider two invariant solutions Phi, Phi_D of the pentagon equation for g and g_D respectively. Motivated by the theory of quasi-Coxeter quasitriangular quasibialgebras \cite{TL3}, we study in this paper the existence of a relative twist, that is an element F invariant under l_D such that the twist of Phi by F is Phi_D. Adapting the method of Donin and Shnider, who treated the case of an empty D, so that l_D=h and Phi_D=1, we give a cohomological construction of such an F under the assumption that Phi_D is the image of Phi under the generalised Harish-Chandra homomorphism. We also show that F is unique up to a gauge transformation if l_D is of corank 1 or F satisfies F^\Theta= F^{21} where \Theta is an involution of g acting as -1 on h.; Comment: minor touch-ups, to appear in Advances in Math

## Cohomological equations for suspension flows over Vershik automorphisms

Zubov, Dmitry
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.15%
In this paper we give sufficient conditions for existence of a solution of cohomological equation for suspension flows over automorphisms of Markov compacta, which were introduced by Vershik and Ito. The main result (Theorem 1) can be regarded as a symbolic analogue of results due to Forni and Marmi, Moussa and Yoccoz for translation flows and interval exchange transformations.; Comment: 10 pp. Comments are welcome! ver.2: small corrections are made

## The cohomological equation for Roth type interval exchange maps

Marmi, Stefano; Moussa, Pierre; Yoccoz, Jean-Christophe
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.56%
We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of Roth type'' imposed to an acceleration of the Rauzy--Veech--Zorich continued fraction expansion associated to T. CONTENTS 0. Introduction 1. The continued fraction algorithm for interval exchange maps 1.1 Interval exchnge maps 1.2 The continued fraction algorithm 1.3 Roth type interval exchange maps 2. The cohomological equation 2.1 The theorem of Gottschalk and Hedlund 2.2 Special Birkhoff sums 2.3 Estimates for functions of bounded variation 2.4 Primitives of functions of bounded variation 3. Suspensions of interval exchange maps 3.1 Suspension data 3.2 Construction of a Riemann surface 3.3 Compactification of $M_\zeta^*$ 3.4 The cohomological equation for higher smoothness 4. Proof of full measure for Roth type 4.1 The basic operation of the algorithm for suspensions 4.2 The Teichm\"uller flow 4.3 The absolutely continuous invariant measure 4.4 Integrability of $\log\Vert Z_{(1)}\Vert$ 4.5 Conditions (b) and (c) have full measure 4.6 The main step 4.7 Condition (a) has full measure 4.8 Proof of the Proposition Appendix A Roth--type conditions in a concrete family of i.e.m. Appendix B A non--uniquely ergodic i.e.m. satsfying condition (a) References; Comment: 64 pages...

## BCOV theory via Givental group action on cohomological field theories

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.15%
In a previous paper (arXiv:0704.1001), Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV equation, based on the earlier paper of Bershadsky, Cecotti, Ooguri, and Vafa. In the present paper, we give an interpretation of this full descendant potential in terms of Givental group action on cohomological field theories. In particular, the fact that it satisfies all tautological equations becomes a trivial observation.; Comment: 22 pages

## Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach

Bizdadea, C.; Cioroianu, E. M.; Saliu, S. O.; Sararu, S. C.; Iordache, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.15%
The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a free model that describes a massless Rarita-Schwinger theory and an Abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.; Comment: 59 pages

## H\"older regularity of the solutions of the cohomological equation for Roth type interval exchange maps

Marmi, Stefano; Yoccoz, Jean-Christophe
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.27%
We prove that the solutions of the cohomological equation for Roth type interval exchange maps are H\"older continuous provided that the datum is of class $C^r$ with $r>1$ and belongs to a finite-codimension linear subspace.; Comment: 22 pages

## The Cohomological Equation and Invariant Distributions for Horocycle Maps

Tanis, James
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.27%
We study the invariant distributions for the horocycle map on $\Gamma\backslash SL(2, \mathbb{R})$ and prove Sobolev estimates for the cohomological equation of the horocycle map. As an application, we obtain an estimate for the rate of equidistribution for horocycle maps on compact manifolds.; Comment: 44 pages

## Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.27%

## Interacting mixed-symmetry type tensor gauge fields of degrees two and three: a four-dimensional cohomological approach

Bizdadea, C.; Ciobirca, C. C.; Cioroianu, E. M.; Saliu, S. O.; Sararu, S. C.
Tipo: Artigo de Revista Científica
A special class of mixed-symmetry type tensor gauge fields of degrees two and three in four dimensions is investigated from the perspective of the Lagrangian deformation procedure based on cohomological BRST techniques. It is shown that the deformed solution to the master equation can be taken to be nonvanishing only at the first order in the coupling constant. As a consequence, we deduce an interacting model with deformed gauge transformations, an open gauge algebra and undeformed reducibility functions. The resulting coupled Lagrangian action contains a quartic vertex and some mass'' terms involving only the tensor of degree two. We discuss in what sense the results of the deformation procedure derived here are complementary to recent others.; Comment: LaTeX 2.e, 10 pages