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A. Alexandrov

Publications and source records attributed to A. Alexandrov.

49 records · Page 3Linked to original sources
arXiv2009

BGWM as Second Constituent of Complex Matrix Model

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).

hep-th↗
arXiv2009

To Cavity EM-Field Quantization

Cavity QED canonical quantization theory is developed, taking into consideration the dual symmetry of Maxwell equations. The expression for the charge quantum is established for the first time.

quant-ph↗
arXiv2009

Dual Symmetric Solution of Maxwell Equations and Correct Quantization of Electromagnetic Field

It has been found, that free electromagnetic (EM) field in restricted volume (typical experimental case) consists of two independent and equally possible components with different parity under spatial inversion transformations. Either of the two components indicated represents the system of also two independent and equally possible fields, which are even and uneven under time reversal transformations. The rules for local quantization of EM-field in Minkowski space are obtained.

quant-ph↗
arXiv2009

Symmetry Properties of Electromagnetic Field in the Matter

The sets ${Φ({F}^{μν})}, {Φ(\tilde {F}^{μν})}$ of linear functionals on the space $< F,+,\cdot >$ represent themself linear space $< Φ,+,\cdot >$ over the field of \textit{scalars} $P$, which is dual to space $< F,+,\cdot >$, but it is substantial, that given linear space is not self-dual. It has been found, that the partition of linear space $< F,+,\cdot >$ over the field of genuine scalars and pseudoscalars, the vectors in which are sets of contravariant and covariant electromagnetic field tensors and pseudotensors ${{F}^{μν}}$, ${\tilde{F}^{μν}}$, ${{F}_{μν}}$, ${\tilde{F}_{μν}}$, on 4 subspaces takes place. It corresponds to appearance of 4 kinds of electromagnetic field potential 4-vectors $A_μ$, which are transformed according to the representations of general Lorentz group with various symmetry relatively improper rotations. It has been found, that conserving quantity, corresponding to complex fields is complex charge. It is argued, that electromagnetic field in the matter is complex field and that two-parametric group $Γ(α,β) = U_{1}(α) \otimes \mathfrak R(β)$, where $\mathfrak R(β)$ is abelian multiplicative group of real numbers (excluding zero), determines the gauge symmetry of electromagnetic field. It is also argued, that free electromagnetic field is characterized by pure imagine charge.

physics.class-ph↗
arXiv2008

Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model

In arXiv:hep-th/0310113 we started a program of creating a reference-book on matrix-model tau-functions, the new generation of special functions, which are going to play an important role in string theory calculations. The main focus of that paper was on the one-matrix Hermitian model tau-functions. The present paper is devoted to a direct counterpart for the Kontsevich and Generalized Kontsevich Model (GKM) tau-functions. We mostly focus on calculating resolvents (=loop operator averages) in the Kontsevich model, with a special emphasis on its simplest (Gaussian) phase, where exists a surprising integral formula, and the expressions for the resolvents in the genus zero and one are especially simple (in particular, we generalize the known genus zero result to genus one). We also discuss various features of generic phases of the Kontsevich model, in particular, a counterpart of the unambiguous Gaussian solution in the generic case, the solution called Dijkgraaf-Vafa (DV) solution. Further, we extend the results to the GKM and, in particular, discuss the p-q duality in terms of resolvents and corresponding Riemann surfaces in the example of dualities between (2,3) and (3,2) models.

hep-th↗
arXiv2006

Instantons and Merons in Matrix Models

Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z_G and Kontsevich tau-functions Z_K. In physical terms, this decomposition is the matrix-model version of multi-instanton and multi-meron configurations in Yang-Mills theories. Technically, decomposition formulas are related to representation theory of algebras of Krichever-Novikov type on families of spectral curves with additional Seiberg-Witten structure. Representations of these algebras are encoded in terms of "the global partition functions". They interpolate between Z_G and Z_K associated with different singularities on spectral Riemann surfaces. This construction is nothing but M-theory-like unification of various matrix models with explicit and representative realization of dualities.

hep-th↗
arXiv2006

M-Theory of Matrix Models

Small M-theories unify various models of a given family in the same way as the M-theory unifies a variety of superstring models. We consider this idea in application to the family of eigenvalue matrix models: their M-theory unifies various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition functions) with Kontsevich tau-function. Moreover, the corresponding duality relations look like direct analogues of instanton and meron decompositions, familiar from Yang-Mills theory.

hep-th↗
arXiv2004

Solving Virasoro Constraints in Matrix Models

This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. These equations are parameterized by a degree n polynomial W_n(x), and the general solution is labeled by an arbitrary function of n-1 coefficients of the polynomial. We also discuss in this general framework a special class of (multi-cut) solutions recently studied in the context of \cal N=1 supersymmetric gauge theories.

hep-th↗
arXiv2004

Unified description of correlators in non-Gaussian phases of Hermitean matrix model

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of non-Gaussian phases of the Hermitean one-matrix model. A unified approach is proposed for description of "connected correlators" in the form of the phase-independent "check-operators" acting on the small space of T-variables (which parameterize the polynomial W(z)). With appropriate definitions and ordering prescriptions, the multidensity check-operators look very similar to the Gaussian case (however, a reliable proof of suggested explicit expressions in all loops is not yet available, only certain consistency checks are performed).

hep-th↗
arXiv2002

Givental formula in terms of Virasoro operators

We present a conjecture that the universal enveloping algebra of differential operators $\frac{\p}{\p t_k}$ over $\mathbb{C}$ coincides in the origin with the universal enveloping algebra of the (Borel subalgebra of) Virasoro generators from the Kontsevich model. Thus, we can decompose any (pseudo)differential operator to a combination of the Virasoro operators. Using this decomposition we present the r.h.s. of the Givental formula math.AG/0008067 as a constant part of the differential operator we introduce. In the case of $\mathbb{CP}^1$ studied in hep-th/0103254, the l.h.s. of the Givental formula is a unit, which imposes certain constraints on this differential operator. We explicitly check that these constraints are correct up to $O(q^4)$. We also propose a conjecture of factorization modulo Hirota equation of the differential operator introduced and check this conjecture with the same accuracy.

hep-th↗
arXiv2001

Test for the Myers-Chern-Simons Action

We present a generalization of the infinitesimal gauge transformation for nonabelian fields on the stack of branes up to the third order in $Φ$. We test the gauge invariance of the action up to the fifth order in $Φ$ for $D$-instantons. This substantiates the Myers formula for the Chern-Simons term in action, which describes interaction with the RR fields of $N$ coincident $\Dp$ branes.

hep-th↗