scholarly journals On the marginally relevant operator in z = 2 Lifshitz holography

2014 ◽  
Vol 2014 (3) ◽  
Author(s):  
Kristian Holsheimer
Keyword(s):  
Relevant Operator

CLASSES OF SEQUENTIALLY LIMITED OPERATORS

2015 ◽  
Vol 58 (3) ◽  
pp. 573-586
Author(s):  
JAN H. FOURIE ◽  
ELROY D. ZEEKOEI
Keyword(s):  
Banach Space ◽  
Vector Space ◽  
Normed Space ◽  
Operator Ideal ◽  
Operator Ideals ◽  
Ideal Norm ◽  
Relevant Operator

AbstractThe purpose of this paper is to present a brief discussion of both the normed space of operator p-summable sequences in a Banach space and the normed space of sequentially p-limited operators. The focus is on proving that the vector space of all operator p-summable sequences in a Banach space is a Banach space itself and that the class of sequentially p-limited operators is a Banach operator ideal with respect to a suitable ideal norm- and to discuss some other properties and multiplication results of related classes of operators. These results are shown to fit into a general discussion of operator [Y,p]-summable sequences and relevant operator ideals.

BLACK HOLE THERMODYNAMIC FLUCTUATIONS AND PHASE TRANSITION OF IR MODIFIED HOŘAVA–LIFSHITZ GRAVITY

2014 ◽  
Vol 23 (03) ◽  
pp. 1450027
Author(s):  
SHIWEI ZHOU ◽  
ZHENFENG NIU ◽  
YAN LÜ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Black Hole Solution ◽  
Three Dimensional ◽  
Nonequilibrium Thermodynamic ◽  
3D Geometry ◽  
Lifshitz Theory ◽  
The Common ◽  
Renormalizable Model ◽  
Relevant Operator

Hořava–Lifshitz theory as a renormalizable model of gravity might be an ultraviolet (UV) completion of general relativity (GR) and it reduces to Einstein gravity with a nonvanishing cosmological constant in infrared (IR) approximation. Kehagias and Sfetsos have added a relevant operator proportional to the three-dimensional (3D) geometry Ricci scalar to the original Hořava–Lifshitz theory action and obtained a spherically symmetric asymptotically flat black hole solution called Kehagias–Sfetsos (KS) black hole. Nonequilibrium thermodynamic fluctuations based on the metric of a KS black hole in IR modified Hořava–Lifshitz gravity have been calculated. It is concluded that the second-order momentum of mass flux is nondivergent and phase transition does not occur at the extremal case, while phase transition occurs at some other case, which is also different from the common case when the heat capacity is divergent.

HIGHER INTEGRALS OF MOTION IN A PERTURBED k = 1 SU(2) WESS-ZUMINO-WITTEN THEORY

1990 ◽  
Vol 05 (11) ◽  
pp. 823-830 ◽  
Author(s):  
KEN-ICHIRO KOBAYASHI ◽  
TSUNEO UEMATSU
Keyword(s):  
Perturbation Theory ◽  
Integrals Of Motion ◽  
Perturbed System ◽  
Witten Theory ◽  
Special Case ◽  
Conserved Currents ◽  
Relevant Operator

We investigate higher integrals of motion in the k = 1 SU(2) Wess-Zumino-Witten (WZW) model perturbed by a certain relevant operator. While the perturbed system is a special case of a Sine-Gordon theory, it is shown to the lowest order in perturbation theory that there exist extra conserved currents due to the SU(2) symmetry in the original WZW model.

scholarly journals INTEGRABLE PERTURBATIONS OF CFT WITH COMPLEX PARAMETER: THE M3/5 MODEL AND ITS GENERALIZATIONS

1996 ◽  
Vol 11 (04) ◽  
pp. 677-697 ◽  
Author(s):  
F. RAVANINI ◽  
M. STANISHKOV ◽  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Minimal Model ◽  
Previous Literature ◽  
Coupling Constant ◽  
Minimal Models ◽  
Thermodynamic Bethe Ansatz ◽  
Bare Coupling ◽  
Bare Coupling Constant ◽  
Ansatz Approach ◽  
Relevant Operator

By using the thermodynamic Bethe ansatz approach, we give evidence of the existence of both massive and massless behaviors for the ϕ2,1 perturbation of the M3,5 nonunitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviors correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of nonunitary minimal models Mp,2p±1, perturbed by their least relevant operator, lead to a cascade of flows similar to that of unitary minimal models perturbed by ϕ1,3. Various aspects and generalizations of this phenomenon and the links with the Izergin–Korepin model are discussed.

On the generalization of density topologies on the real line

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Jacek Hejduk ◽  
Renata Wiertelak
Keyword(s):  
Real Line ◽  
Density Theorem ◽  
Density Topology ◽  
The Real ◽  
Lebesgue Density ◽  
The Family ◽  
Real Anal ◽  
Similarities And Differences ◽  
Relevant Operator

AbstractThe paper concerns the density points with respect to the sequences of intervals tending to zero in the family of Lebesgue measurable sets. It shows that for some sequences analogue of the Lebesgue density theorem holds. Simultaneously, this paper presents proof of theorem that for any sequence of intervals tending to zero a relevant operator ϕJ generates a topology. It is almost but not exactly the same result as in the category aspect presented in [WIERTELAK, R.: A generalization of density topology with respect to category, Real Anal. Exchange 32 (2006/2007), 273–286]. Therefore this paper is a continuation of the previous research concerning similarities and differences between measure and category.

Dirichlet problems for fully anisotropic elliptic equations

2016 ◽  
Vol 147 (1) ◽  
pp. 25-60 ◽  
Author(s):  
Giuseppina Barletta ◽  
Andrea Cianchi
Keyword(s):  
Elliptic Equations ◽  
Partial Differential Operator ◽  
Nonlinear Elliptic Equations ◽  
Dirichlet Problems ◽  
Unified Framework ◽  
Nonlinear Elliptic ◽  
Polynomial Type ◽  
General Convex ◽  
Anisotropic Elliptic Equations ◽  
Relevant Operator

The existence of a non-trivial bounded solution to the Dirichlet problem is established for a class of nonlinear elliptic equations involving a fully anisotropic partial differential operator. The relevant operator depends on the gradient of the unknown through the differential of a general convex function. This function need not be radial, nor have a polynomial-type growth. Besides providing genuinely new conclusions, our result recovers and embraces, in a unified framework, several contributions in the existing literature, and augments them in various special instances.

scholarly journals Boundary RG flows for fermions and the mod 2 anomaly

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Boundary Operator ◽  
Majorana Fermions ◽  
Boundary State ◽  
Infra Red ◽  
Boundary Operators ◽  
Relevant Operator

Boundary conditions for Majorana fermions in d=1+1d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N2N Majorana fermions that preserve a U(1)^NU(1)N symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge gg. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by g^2_{IR} / g^2_{UV} = \mathrm{dim} \, \mathcal{O}gIR2/gUV2=dim𝒪, the dimension of the perturbing boundary operator. Any relevant operator necessarily has \mathrm{dim} \, \mathcal{O} < 1dim𝒪<1, ensuring that the central charge decreases in accord with the gg-theorem.

scholarly journals Clark measures and a theorem of Ritt

2018 ◽  
Vol 122 (2) ◽  
pp. 277 ◽  
Author(s):  
Isabelle Chalendar ◽  
Pamela Gorkin ◽  
Jonathan R. Partington ◽  
William T. Ross
Keyword(s):  
Blaschke Product ◽  
Numerical Range ◽  
Blaschke Products ◽  
Finite Blaschke Product ◽  
Shift Operators ◽  
Finite Blaschke Products ◽  
Relevant Operator

We determine when a finite Blaschke product $B$ can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for $B$. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute.

scholarly journals Janus solutions in three-dimensional $$ \mathcal{N} $$ = 8 gauged supergravity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Kevin Chen ◽  
Michael Gutperle
Keyword(s):  
Three Dimensional ◽  
Expectation Value ◽  
Relevant Operator

Abstract Janus solutions are constructed in d = 3, $$ \mathcal{N} $$ N = 8 gauged supergravity. We find explicit half-BPS solutions where two scalars in the SO(1, 8)/SO(8) coset have a nontrivial profile. These solutions correspond on the CFT side to an interface with a position-dependent expectation value for a relevant operator and a source which jumps across the interface for a marginal operator.

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