Searcharxiv⌕ Search

arXiv subjects

D. M. Belov

Publications and source records attributed to D. M. Belov.

12 recordsLinked to original sources
arXiv2003

Witten's Ghost Vertex Made Simple (bc and bosonized ghosts)

First, we diagonalize the bc-ghost 3-string Neumann matrices using the technique described in hep-th/0304158. Their eigenvalues are in complete agreement with the previous authors. Second, we diagonalize the N-string gluing vertices for the bosonized ghost system. And third, we verify the descent and associativity relations for the combined bosonic matter+ghost gluing vertices. We find that in order for these relations to be true, the vertices must be normalized by the factor Z_N. Here Z_N is the partition function of the bosonic matter+ghost CFT on the gluing surface, which is the unit disc with the Neumann boundary conditions and the midpoint cone like singularity specifying by the angle excess π(N-2).

hep-th↗
arXiv2002

Representation of small conformal algebra

In hep-th/0202087 it was argued that the operator L_0 is bad defined in kappa-basis as a kernel operator. Indeed, we show that L_0 is a difference operator. We also find a representation of L_1 and L_{-1} in a class of difference operators.

hep-th↗
arXiv2002

On spectral density of Neumann matrices

In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log L)/(2π). In this paper we find an exact analytic expression for the finite part of the spectral density. This function allows one to calculate finite parts of various determinants arising in string field theory computations. We put our result to some consistency checks.

hep-th↗
arXiv2002

On Continuous Moyal Product Structure in String Field Theory

We consider a diagonalization of Witten's star product for a ghost system of arbitrary background charge and Grassmann parity. To this end we use a bosonized formulation of such systems and a spectral analysis of Neumann matrices. We further identify a continuous Moyal product structure for a combined ghosts+matter system. The normalization of multiplication kernel is discussed.

hep-th↗
arXiv2002

Construction of the Vacuum String Field Theory on a non-BPS Brane

In the framework of the Sen conjectures a construction of vacuum superstring field theory on a non-BPS brane is discussed. A distinguished feature of this theory is a presence of a ghost kinetic operator mixing GSO+/- sectors. A candidate for such kinetic operator with zero cohomology is discussed.

hep-th↗
arXiv2002

Diagonal Representation of Open String Star and Moyal Product

We explicitly find the spectrum of the operators $M^{rs}$ and $\widetilde{M}^{rs}$, which specify the star-product in the matter and ghost sectors correspondingly. Further we derive the diagonal representation for the 3-string vertices. Using this representation we identify the appearing Moyal structures in the matter sector. In addition to the continuous non-commutativity parameter $θ(κ)$ found in hep-th/0202087 we find the discrete non-commutativity parametrized by $θ_ξ$.

hep-th↗
arXiv2002

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, ``comma'' and matrix representations of vertices.

hep-th↗
arXiv2001

Gauge Invariance and Tachyon Condensation in Cubic Superstring Field Theory

The gauge invariance of cubic open superstring field theory is considered in a framework of level truncation, and applications to the tachyon condensation problem are discussed. As it is known, in the bosonic case the Feynman-Siegel gauge is not universal within the level truncation method. We explore another gauge that is more suitable for calculation of the tachyon potential for fermionic string at level (2,6). We show that this new gauge has no restrictions on the region of its validity at least at this level.

hep-th↗
arXiv2001

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.

hep-th↗
arXiv2000

UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)

We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a presence of non-integrable IR singularities in noncommutative scalar electrodynamics for general coupling constants. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N=2 SUSY gauge theory.

hep-th↗
arXiv2000

A Note on UV/IR for Noncommutative Complex Scalar Field

Noncommutative quantum field theory of a complex scalar field is considered. There is a two-coupling noncommutative analogue of U(1)-invariant quartic interaction $(ϕ^*ϕ)^2$, namely $Aϕ^*\starϕ\starϕ^*\starϕ+ Bϕ^*\starϕ^*\starϕ\starϕ$. For arbitrary values of $A$ and $B$ the model is nonrenormalizable. However, it is one-loop renormalizable in two special cases: B=0 and $A=B$. Furthermore, in the case B=0 the model does not suffer from IR divergencies at least at one-loop insertions level.

hep-th↗