相关论文: On the Liouville coupling constants

The recently proposed expression for the general three point function of exponential fields in quantum Liouville theory on the sphere is considered. By exploiting locality or crossing symmetry in the case of those four-point functions,…

Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…

We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6j-symbols for U_q(sl_N). The expression is a natural generalization of the quantum 6j-symbols for U_q(sl_2) obtained by Kirillov and Reshetikhin.…

Higher-order vertices at zero external momenta for the scalar field theory describing the critical behaviour of the Ising model are studied within the field-theoretical renormalization group (RG) approach in three dimensions. Dimensionless…

Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a…

A well known recurrence relation for the 6j-symbol of the quantum group su_q(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking…

The problem of the structure constants of the operator product expansions in the minimal models of conformal field theory is revisited. We rederive these previously known constants and present them in the form particularly useful in the…

Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…

Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on the sphere. In a certain physical region, where a real classical…

The renormalized zero-momentum four-point coupling $g_r$ of O(N)-invariant scalar field theories in $d$ dimensions is studied by applying the 1/N expansion and strong coupling analysis. The O(1/N) correction to the $\beta$-function and to…

We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…

The strong coupling constant is one of the fundamental parameters of the standard model of particle physics. In this review I will briefly summarise the theoretical framework, within which the strong coupling constant is defined and how it…

A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of dimension equal to the number of degrees of…

The correspondence between the semiclassical limit of the DOZZ quantum Liouville theory and the Nekrasov-Shatashvili limit of the N = 2 (Omega-deformed) U(2) super-Yang-Mills theories is used to calculate the unknown accessory parameter of…

The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an $\hbar$ expansion of Liouville space generating functions, we show how…

This is Part II of our project on block-weighted planar maps and Liouville quantum duality. Focusing on the scaling properties at the dual critical point, we derive the conditional distribution of the root block size given the total size,…

Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $\alpha_s$.…

We consider positive critical points of Caffarelli-Kohn-Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry…

This paper investigates the relation between colored HOMFLY-PT and Kauffman homology, $\text{SO}(N)$ quantum $6j$-symbols and $(a,t)$-deformed $F_K$. First, we present a simple rule of grading change which allows us to obtain the…

The computation of the correlation numbers in Minimal Liouville Gravity involves an integration over moduli spaces of complex curves. There are two independent approaches to the calculation: the direct one, based on the CFT methods and…