48
48

Sep 21, 2013
09/13

by
Oleg Alekseev

texts

#
eye 48

#
favorite 0

#
comment 0

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed...

Source: http://arxiv.org/abs/1106.4758v2

70
70

Sep 22, 2013
09/13

by
Oleg Alekseev

texts

#
eye 70

#
favorite 0

#
comment 0

We propose a free field representation for the form factors of descendant operators in the Bullough-Dodd model. This construction is a particular modification of Lukyanov's technique for solving the form factors axioms. We prove that the number of proposed solutions in each level subspace of the chiral sectors coincide with the number of the corresponding descendant operators in the Lagrangian formalism. We check that these form factors possess the cluster factorization property. Besides, we...

Source: http://arxiv.org/abs/1210.2818v2

10
10.0

Jun 27, 2018
06/18

by
Oleg Alekseev; Fábio Novaes

texts

#
eye 10

#
favorite 0

#
comment 0

Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for $W_N$ conformal blocks with one component in the fundamental representation and another in a rectangular representation of $SU(N)$, which can be used to obtain...

Topics: Mathematical Physics, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1505.06221

77
77

Sep 17, 2013
09/13

by
Oleg Alekseev; Michael Lashkevich

texts

#
eye 77

#
favorite 0

#
comment 0

In the framework of the free field representation we obtain exact form factors of local operators in the two-dimensional affine Toda theories of the $A^{(1)}_{L-1}$ series. The construction generalizes Lukyanov's well-known construction to the case of descendant operators. Besides, we propose a free field representation with a countable number of generators for the `stripped' form factors, which generalizes the recent proposal for the sine/sinh-Gordon model. As a check of the construction we...

Source: http://arxiv.org/abs/0912.5225v4

5
5.0

Jun 29, 2018
06/18

by
Oleg Alekseev; Mark Mineev-Weinstein

texts

#
eye 5

#
favorite 0

#
comment 0

A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The classical point for the action, defined as a minus logarithm of the growth probability, describes the most probable scenario and reproduces the Laplacian growth equation, which embraces numerous fundamental free boundary dynamics in non-equilibrium physics. For...

Topics: Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Nonlinear Sciences,...

Source: http://arxiv.org/abs/1604.06822