Alexei Morozov

Alexei Morozov
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High Energy Physics - Theory (12)
 
Mathematics - Mathematical Physics (5)
 
Mathematical Physics (5)
 
High Energy Physics - Phenomenology (3)
 
General Relativity and Quantum Cosmology (2)
 
Mathematics - Representation Theory (2)
 
Mathematics - Geometric Topology (2)
 
Mathematics - Quantum Algebra (2)
 
High Energy Physics - Lattice (1)

Publications Authored By Alexei Morozov

We derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki (DIM) algebra U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1). We demonstrate that certain refined topological string amplitudes satisfy these equations and find that the braiding transformations are performed by the R-matrix of U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1). The resulting syste is the uplifting of the \widehat{\mathfrak{u}}_1 Wess-Zumino-Witten model. Read More

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the Yangian case by A.~Smirnov but less general. Read More

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity. Read More

Following the suggestion of arXiv:1407.6319 to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an infinite series of twist-like virtual knots and antiparallel 2-strand links. Within this family one can check topological invariance and understand how differential hierarchy is modified in virtual case. Read More

Virtual knots are associated with knot diagrams, which are not obligatory planar. The recently suggested generalization from N=2 to arbitrary N of the Kauffman-Khovanov calculus of cycles in resolved diagrams can be straightforwardly applied to non-planar case. In simple examples we demonstrate that this construction preserves topological invariance -- thus implying the existence of HOMFLY extension of cabled Jones polynomials for virtual knots and links. Read More

In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing points of the contours projection on the xy plane contribute. Though the theory is quadratic, P-exponents remain non-trivial operators and R-factors are easier to guess then derive. Read More

We perform a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension. These theories are well known to possess very unusual properties, unfamiliar from studies of gauge and Lorentz invariant models. These peculiarities are caused by mixing of familiar transverse fields with revived longitudinal and pure gauge (Stueckelberg) fields and are all seen already in quadratic approximation. Read More

We analyze the pattern of normal modes in linearized Lorentz-violating massive gravity over the 5-dimensional moduli space of mass terms. Ghost-free theories arise at bifurcation points when the ghosts get out of the spectrum of propagating particles due to vanishing of the coefficient in front of \omega^2 in the propagator. Similarly, the van Dam-Veltman-Zakharov (DVZ) discontinuities in the Newton law arise at another type of bifurcations, when the coefficient vanishes in front of \vec k^2. Read More

An explicit check of the AGT relation between the W_N-symmetry controlled conformal blocks and U(N) Nekrasov functions requires knowledge of the Shapovalov matrix and various triple correlators for W-algebra descendants. We collect simplest expressions of this type for N=3 and for the two lowest descendant levels, together with the detailed derivations, which can be now computerized and used in more general studies of conformal blocks and AGT relations at higher levels. Read More

The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. Read More

A representation of the group element (also known as ``universal ${\cal T}$-matrix'') which satisfies $\Delta(g) = g\otimes g$, is given in the form $$ g = \left(\prod_{s=1}^{d_B}\phantom.^>\ {\cal E}_{1/q_{i(s)}}(\chi^{(s)}T_{-i(s)})\right) q^{2\vec\phi\vec H} \left(\prod_{s=1}^{d_B}\phantom.^<\ {\cal E}_{q_{i(s)}}(\psi^{(s)} T_{+i(s)})\right)$$ where $d_B = \frac{1}{2}(d_G - r_G)$, $q_i = q^{|| \vec\alpha_i||^2/2}$ and $H_i = 2\vec H\vec\alpha_i/||\vec\alpha_i||^2$ and $T_{\pm i}$ are the generators of quantum group associated respectively with Cartan algebra and the {\it simple} roots. Read More

We describe a representation of the $q$--hypergeometric functions of one variable in terms of correlators of vertex operators made out of free scalar fields on the Riemann sphere. Read More