scholarly journals TOPOLOGICAL CONFORMAL FIELD THEORY WITH A RATIONAL W POTENTIAL AND THE DISPERSIONLESS KP HIERARCHY

1994 ◽  
Vol 09 (27) ◽  
pp. 2481-2492 ◽  
Author(s):  
S. AOYAMA ◽  
Y. KODAMA
Keyword(s):  
Specific Form ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Kp Hierarchy ◽  
Large Space ◽  
Conformal Field ◽  
New Class ◽  
Small Phase ◽  
Large Phase ◽  
Topological Conformal Field Theory

We present a new class of topological conformal field theories (TCFTs) characterized by a rational W potential, which includes the minimal models of A and D types as its subclasses. An explicit form of the W potential is found by solving the underlying dispersionless KP hierarchy in a particular small phase space. We also discuss the dispersionless KP hierarchy in large phase spaces by reformulating the hierarchy, and show that the W potential takes a universal form, which does not depend on a specific form of the solution in a large space.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

THE ANNIHILATING IDEALS OF MINIMAL MODELS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 217-238 ◽  
Author(s):  
BORIS L. FEIGIN ◽  
TOMOKI NAKANISHI ◽  
HIROSI OOGURI
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Finite Models ◽  
Conformal Field ◽  
Intimate Relation ◽  
Chiral Algebras

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals $\bm{\widehat{{\rm U}(1)}\times\widehat{{\rm SU}({\lc m})}_{1}}$ THEORY AND c=m W1+∞ MINIMAL MODELS IN THE HIERARCHICAL QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (06) ◽  
pp. 915-926 ◽  
Author(s):  
MARINA HUERTA
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Quantum Hall ◽  
Detailed Comparison ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Group Flow

Two classes of Conformal Field Theories have been proposed to describe the Hierarchical Quantum Hall Effect: the multicomponent bosonic theory, characterized by the symmetry [Formula: see text] and the W1+∞ minimal models with central charge c=m. In spite of having the same spectrum of edge excitations, they manifest differences in the degeneracy of the states and in the quantum statistics, which call for a more detailed comparison between them. Here, we describe their detailed relation for the general case, c=m and extend the methods previously published for c≤3. Specifically, we obtain the reduction in the number of degrees of freedom from the multicomponent Abelian theory to the minimal models by decomposing the characters of the [Formula: see text] representations into those of the c=mW1+∞ minimal models. Furthermore, we find the Hamiltonian whose renormalization group flow interpolates between the two models, having the W1+∞ minimal models as an infrared fixed point.

scholarly journals Coset construction of Virasoro minimal models and coupling of Wess–Zumino–Witten theory with Schramm–Loewner evolution

2019 ◽  
Vol 31 (10) ◽  
pp. 1950037
Author(s):  
Shinji Koshida
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Loewner Evolution ◽  
Witten Theory ◽  
Coset Construction ◽  
New Perspective ◽  
Group Symmetries ◽  
Math Phys

Schramm–Loewner evolution (SLE) is a random process that gives a useful description of fractal curves. After its introduction, many works concerning the connection between SLE and conformal field theory (CFT) have been carried out. In this paper, we develop a new method of coupling SLE with a Wess–Zumino–Witten (WZW) model for [Formula: see text], an example of CFT, relying on a coset construction of Virasoro minimal models. Generalizations of SLE that correspond to WZW models were proposed by previous works [E. Bettelheim et al., Stochastic Loewner evolution for conformal field theories with Lie group symmetries, Phys. Rev. Lett. 95 (2005) 251601] and [Alekseev et al., On SLE martingales in boundary WZW models, Lett. Math. Phys. 97 (2011) 243–261], in which the parameters in the generalized SLE for [Formula: see text] were related to the level of the corresponding [Formula: see text]-WZW model. The present work unveils the mechanism of how the parameters were chosen, and gives a simpler proof of the result in these previous works, shedding light on a new perspective of SLE/WZW coupling.

scholarly journals On Fusion Rules in Logarithmic Conformal Field Theories

1997 ◽  
Vol 12 (10) ◽  
pp. 1943-1958 ◽  
Author(s):  
Michael A. I. Flohr
Keyword(s):  
Quantum Group ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Group Representations ◽  
Fusion Rules ◽  
Conformal Field ◽  
Almost All

We find the fusion rules for the cp,1 series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance of negative fusion coefficients which can be understood in terms of exceptional quantum group representations. The effective fusion rules (i.e. without signs and multiplicities) resemble the BPZ fusion rules for the virtual minimal models with conformal grid given via c = c3p,3. This leads to the conjecture that (almost) all minimal models with c = cp,q, gcd (p,q) > 1, belong to the class of rational logarithmic conformal field theories.

scholarly journals Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
John Cardy
Keyword(s):  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Boundary State ◽  
Variational Approximations ◽  
The Matrix ◽  
Boundary States ◽  
Quantum Quenches ◽  
Explicit Formulae ◽  
Renormalization Group Flows

We propose using smeared boundary states e^{-\tau H}|\cal B\rangle as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.

NON-UNITARY SUPERSYMMETRIC CONFORMAL FIELD THEORIES AND SUPERSYMMETRIC SINE-GORDON EQUATION

1990 ◽  
Vol 05 (25) ◽  
pp. 2071-2077 ◽  
Author(s):  
SOONKEON NAM
Keyword(s):  
Gordon Equation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Sine Gordon Equation ◽  
Moody Algebra ◽  
Superconformal Field Theories ◽  
Conformal Field ◽  
The Family ◽  
Coset Construction

We study coset construction of superconformal minimal models using admissible representations of Kac-Moody algebra. In particular, we study supersymmetric minimal models of Wn algebra, and in particular we argue that c = −5/2 cannot be considered as a minimal model of superconformal or super-W3 algebra. In the second part of the paper, we consider superconformal field theories whose perturbations correspond to breather-breather scattering in supersymmetric sine-Gordon equations, and find a family of theories with c = −3N(4N + 3)/2(N + 1), N = 1, 2, 3, …, which is the counterpart of the family of non-unitary theories with c = −2N(6N + 5)/(2N + 3), N = 1, 2, 3, …, among which N = 1 (c = −22/5) is the Yang-Lee edge singularity.

scholarly journals SINE-GORDON VS. MASSIVE THIRRING

1993 ◽  
Vol 08 (23) ◽  
pp. 4131-4174 ◽  
Author(s):  
TIMOTHY R. KLASSEN ◽  
EZER MELZER
Keyword(s):  
Energy Levels ◽  
Gaussian Model ◽  
Field Theories ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Fermion Fields ◽  
S Matrix

By viewing the sine-Gordon and massive Thirring models as perturbed conformal field theories, one sees that they are different (the difference being observable, for instance, in finite-volume energy levels). The UV limit of the former (SGM) is a Gaussian model, that of the latter (MTM) a so-called fermionic Gaussian model, the compactification radius of the boson underlying both theories depending on the SG/MT coupling. (These two families of conformal field theories are related by a “twist”.) Corresponding SG and MT models contain a subset of fields with identical correlation functions, but each model also has fields the other one does not have; for example, the fermion fields of MTM are not contained in SGM, and the bosonic soliton fields of SGM are not in MTM. Our results imply, in particular, that the SGM at the so-called “free-Dirac point” β2=4π is actually a theory of two interacting bosons with diagonal S-matrix S=−1, and that for arbitrary couplings the overall sign of the accepted SG S-matrix in the soliton sector should be reversed. More generally, we draw attention to the existence of new classes of quantum field theories, analogs of the (perturbed) fermionic Gaussians models, whose partition functions are invariant only under a subgroup of the modular group. One such class comprises “fermionic versions” of the Virasoro minimal models.

scholarly journals Conformal Properties of Hyperinvariant Tensor Networks

2021 ◽  
Author(s):  
Matthew Steinberg ◽  
Javier Prior
Keyword(s):  
Spin Chain ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Tensor Decompositions ◽  
Numerical Evidence ◽  
Conformal Field ◽  
New Class ◽  
Tensor Networks ◽  
Original Construction

Abstract Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence. Although this new class of network shows much potential for simulating conformal field theories on hyperbolic bulk manifolds with quasiperiodic boundaries, many issues must still be solved. In this manuscript we analyze the challenges related to optimizing tensors in a hyMERA with respect to some critical spin chain, and compare with standard approaches in MERA. Additionally, we show two new sets of tensor decompositions which exhibit different properties from the original construction, and imply that the multitensor constraints are more general than previously suggested. Lastly, we provide numerical evidence that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra for many minimial model CFTs.

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