QUASI-EXACTLY-SOLVABLE QUANTAL PROBLEMS: ONE-DIMENSIONAL ANALOGUE OF RATIONAL CONFORMAL FIELD THEORIES

1990 ◽  
Vol 05 (04) ◽  
pp. 803-832 ◽  
Author(s):  
A. YU. MOROZOV ◽  
A.M. PERELOMOV ◽  
A.A. ROSLY ◽  
M.A. SHIFMAN ◽  
A.V. TURBINER
Keyword(s):  
Mathematical Formulation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Solvable Models ◽  
One Dimensional ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Shed Light ◽  
Ordinary Quantum

The class of quasi-exactly-solvable problems in ordinary quantum mechanics discovered recently shows remarkable parallels with rational two-dimensional conformal field theories. This fact suggests that investigation of the quasi-exactly-solvable models may shed light on rational conformal field theories. We discuss a relation between these two theoretical schemes and propose a mathematical formulation for the procedure of constructing quasi-exactly solvable systems. This discussion leads us to a kind of generalization of the Sugawara construction.

BRAIDS, LINK POLYNOMIALS AND TRANSFORMATIONS OF SOLVABLE MODELS

1990 ◽  
Vol 05 (11) ◽  
pp. 2195-2239 ◽  
Author(s):  
TETSUO DEGUCHI
Keyword(s):  
Solvable Model ◽  
Field Theories ◽  
Exactly Solvable Models ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Solvable Models ◽  
Conformal Field ◽  
Topological Quantum ◽  
Exactly Solvable ◽  
Infinitesimal Operators

It is shown that braid matrices and link polynomials can be systematically constructed from exactly solvable models in statistical mechanics. Through symmetry breaking transformations, different braid matrices are derived from a solvable model. By associating the Markov traces with multi-variable representations, multi-variable link polynomials are obtained. Infinitesimal operators for braid matrices are constructed. Connection of our approach to the conformal field theories and the topological quantum field theory is discussed.

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.

QUASI-EXACTLY SOLVABLE PROBLEMS AND SU(1,1) GROUP

1994 ◽  
Vol 09 (16) ◽  
pp. 1501-1505 ◽  
Author(s):  
O.B. ZASLAVSKII
Keyword(s):  
Lie Algebra ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Infinite Dimensional Representation

It is shown that the particular class of one-dimensional quasi-exactly solvable models can be constructed with the help of infinite-dimensional representation of Lie algebra. Hamiltonian of a system is expressed in terms of SU(1,1) generators.

scholarly journals Negativity spectrum of one-dimensional conformal field theories

2016 ◽  
Vol 94 (19) ◽  
Author(s):  
Paola Ruggiero ◽  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
One Dimensional ◽  
Conformal Field

CRITICAL RSOS MODELS AND CONFORMAL FIELD THEORY

1989 ◽  
Vol 04 (01) ◽  
pp. 115-142 ◽  
Author(s):  
V. V. BAZHANOV ◽  
N. YU. RESHETIKHIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Critical Behavior ◽  
Field Theories ◽  
Dimensional Chain ◽  
Conformal Field Theories ◽  
One Dimensional ◽  
Conformal Field ◽  
Rsos Models ◽  
The One

The eigenvalues of the transfer matrix of the generalized RSOS model are exactly calculated. From the consideration of the thermodynamics of the quantum system on the one-dimensional chain connected with the RSOS model, we calculate the central charges of the effective conformal field theories describing the critical behavior of the model in different regimes.

RECENT DEVELOPMENTS OF ALGEBRAIC METHODS IN QUANTUM FIELD THEORIES

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2041-2059 ◽  
Author(s):  
B. SCHROER
Keyword(s):  
Algebraic Methods ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
One Dimensional ◽  
Conformal Field ◽  
Recent Developments

Recent results obtained by modular methods concerning the algebraic origin of spacetime covariance from modular and dual properties of causal nets are presented. Particular emphasis is given to one-dimensional nets which are important in the classification of chiral conformal field theories.

scholarly journals MOTIVIC L-FUNCTION IDENTITIES FROM CFT AND ARITHMETIC MIRROR SYMMETRY

2013 ◽  
Vol 28 (36) ◽  
pp. 1350167
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
Zeta Function ◽  
General Result ◽  
Mirror Symmetry ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Affine Invariants ◽  
Exactly Solvable

Exactly solvable mirror pairs of Calabi–Yau threefolds of hypersurface type exist in the class of Gepner models that include nondiagonal affine invariants. Motivated by the string theoretic automorphy established previously for models in this class, it is natural to ask whether the arithmetic structure of mirror pairs varieties reflects the fact that as conformal field theories, they are isomorphic. Mirror symmetry in particular predicts that the L-functions of the Ω-motives of such pairs are identical. In this paper this prediction is confirmed by showing that the Ω-motives of exactly solvable mirror pairs are isomorphic. This follows as a corollary of the proof of a more general result establishing an isomorphism between nondiagonally and diagonally induced motives in this class of varieties. The motivic approach formulated here circumvents the difficulty that no mirror construction of the Hasse–Weil zeta function is known.

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.

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