arXiv subjects

Dimitri Polyakov

Publications and source records attributed to Dimitri Polyakov.

At least 19 recordsLinked to original sources

arXiv2019

Solutions for Mixed States in Open Bosonic String Theory

We describe the family of normalizable solutions in linearized open string field theory, defined by $Q\Psi_0=0$ ($Q$ is BRST charge) understood in the sense $< >=0$ for an arbitrary string field $\Phi$. The solutions depend on shifted partition numbers and are parametrized in terms of values of $\zeta$-function at pairs of positive numbers greater than 2. We argue that the operators, defined by these solutions, create mixed quantum-mechanical states by acting on the vacuum (as opposed to standard vertex operators, creating the pure states with definite masses and spins).

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arXiv2019

Entanglement Entropy from String Field Theory (and a Higher-Spin Example)

We study the new class of solutions in linearized open string field theory (OSFT) involving higher-spin modes. Unlike the elementary OSFT solutions (on-shell vertex operators) that, acting on a vacuum, define wavefunctions of pure states (e.g. a tachyon), the solutions that we describe correspond to the reduced density matrices which eigenvalues describe the entanglement between higher-spin modes with different spin values. We compute the entanglement entropy on these OSFT solutions, and the answer is expressed in terms of converging series in inverse weighted partition numbers. In the case of $D$-dimensional bosonic string theory, the entanglement entropy of spin $1$ subsystem and the system of all the spin values is given by $D{\log{\lambda_0}}+{D\over{\lambda_0}}\sum_{N=3}^\infty{{|\beta(N)|}\over{\lambda(N)}} {\log{({{\lambda(N)}\over{|\beta(N)|}})}}$, where $\lambda(N)$ is the weighted number of partitions of $N$, $\beta(N)={{(N-1)\zeta(3)-\zeta(2)}\over{(N-1)^4}}$ and $\lambda_0=\sum_{N=1}^{\infty}{{\beta(N)}\over{\lambda(N)}}$ ($\zeta$ is Riemann's zeta-function). The first term, $D{\log{\lambda_0}}$, represents the entanglement swapping between string vacuum and string excitations. We generalize this result to obtain the entanglement for a subsystem of a given spin $s$ in a given space-time dimension. We also discuss how open string field theory may be used to study the entanglement of systems other than higher spin excitations in string theory.

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arXiv2018

Higher-Spin Quartic Vertices in AdS5 : a Rectangular Limit

We determine the form of a significantly large class of gauge-invariant quartic vertices for symmetric higher-spin fields (in Vasiliev formalism) in AdS5 space in the rectangular limit, (defined in the paper) using the higher-spin vertex operators in superstring theory, which construction is based on the generators of the higher-spin symmetry algebra, enveloping the AdS isometries. In this limit, a particular simplification is that the quartic vertices do not receive corrections from worldsheet renormalization group flows of the cubic terms, so their structure is fixed directly by the 4-point amplitudes in superstring theory.

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arXiv2017

Interactions of Irregular Gaiotto States in Liouville Theory

We compute the correlation functions of irregular Gaiotto states appearing in the colliding limit of the Liouville theory by using "regularizing" conformal transformations mapping the irregular (coherent) states to regular vertex operators in the Liouville theory. The $N$-point correlation functions of the irregular vertex operators of arbitrary ranks are expressed in terms of $N$-point correlators of primary fields times the factor that involves regularized higher-rank Schwarzians of the above conformal transformation. In particular, in the case of three-point functions the general answer is expressed in terms of DOZZ (Dorn-Otto-Zamolodchikov-Zamolodchikov) structure constants times exponents of regularized higher-derivative Schwarzians. The explicit examples of the regularization are given for the ranks one and two.

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arXiv2017

An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory

We study the correlators of irregular vertex operators in two-dimensional conformal field theory (CFT) in order to propose an exact analytic formula for calculating numbers of partitions, that is: 1) for given $N,k$, finding the total number $\lambda(N|k)$ of length $k$ partitions of $N$: $N=n_1+...+n_k;0<n_1\leq{n_2}...\leq{n_k}$. 2) finding the total number $\lambda(N)=\sum_{k=1}^N\lambda(N|k)$ of partitions of a natural number $N$ We propose an exact analytic expression for $\lambda(N|k)$ by relating two-point short-distance correlation functions of irregular vertex operators in $c=1$ conformal field theory ( the form of the operators is established in this paper): with the first correlator counting the partitions in the upper half-plane and the second one obtained from the first correlator by conformal transformations of the form $f(z)=h(z)e^{-{i\over{z}}}$ where $h(z)$ is regular and non-vanishing at $z=0$. The final formula for $\lambda(N|k)$ is given in terms of regularized ($\epsilon$-ordered) finite series in the generalized higher-derivative Schwarzians and incomplete Bell polynomials of the above conformal transformation at $z=i\epsilon$ ($\epsilon\rightarrow{0}$)

math.NT↗

arXiv2016

Super-spectral curve of irregular conformal blocks

We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the colliding limit of supersymmetric vertex operators of NS sector and half-odd integer to the Ramond sectors. The spectral curve is simply integrable at Nekrasov-Shatashvili limit and the partition function (inner product of irregular conformal state) is obtained from the superconformal structure manifest in the spectral curve. We present some explicit forms of the partition function of integer (NS sector) and of half-odd ranks (Ramond sector).

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arXiv2016

Higher Spins as Rolling Tachyons in Open String Field Theory

We find a simple analytic solution in open string field theory which, in the on-shell limit, generates a tower of higher spin vertex operators in bosonic string theory. The solution is related to irregular off-shell vertex operators for Gaiotto states. The wavefunctions for the irregular vertex operators are described by equations following from the cubic effective action for generalized rolling tachyons, indicating that the evolution from flat to collective higher-spin background in string field theory occurs according to cosmological pattern. We discuss the relation between nonlocalities of the rolling tachyon action and those of higher spin interactions.

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arXiv2016

Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case

We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case: upon supersymmetrization, the irregular operators are no longer the eigenstates of positive Virasoro and $W_N$ generators but block-diagonalize them. We relate the block-diagonal structure of the irregular vertices to contributions of the Ramond sector to the colliding limit.

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arXiv2016

Irregular Vertex Operators for Irregular Conformal Blocks

We construct the free field representation of irregular vertex operators of arbitrary rank which generates simultaneous eigenstates of positive modes of Virasoro and W symmetry generators. The irregular vertex operators turn out to be the exponentials of combinations of derivatives of Liouville or Toda fields, creating irregular coherent states. We compute examples of correlation functions of these operators and study their operator algebra.

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arXiv2015

Higher Spins at the Quintic Order: Localization Effect and Simplifications

We investigate the special case of quintic interactions for massless higher spin gauge fields using the string-theoretic vertex operator construction for higher spin gauge fields in Vasiliev's frame-like formalism. We compute explicitly the related 5-point interaction vertex in the low energy limit of string theory and find that: the structure of the quintic $s_1-s_2-s_3-s_4-s_5$ higher spin interaction gets drastically simplified and localized if a) the spin values satisfy the constraint $s_1+s_2+s_3=s_4+s_5+2$ (and, more generally, if the sum of three spin values roughly equals the sum of the remaining two b) One of the spin values, $s_4$ or $s_5$ is sufficiently small. In this paper, the explicit computation is done for the case $s_4=4$

hep-th↗

arXiv2015

A Note on GSO-Free RNS Superstrings and Pure Spinor Constraint

Using an elementary perturbative open string field theory solution involving a twistor-like parameter, we study the cohomology of new nilpotent BRST charge corresponding to the space-time background defined by this solution. The BRST cohomology of the deformed background automatically cuts off the GSO-odd spectrum in RNS superstring theory and keeps the GSO-even spectrum intact, without a need of GSO-projection. The on-shell constraints in the GSO-even sector get deformed in the new background, corresponding to BRST type transformations of the low-energy effective action with the ghost-like commuting spinor parameter satisfying the pure spinor constraint in $d=10$.

hep-th↗

arXiv2015

Solutions in Bosonic String Field Theory and Higher Spin Algebras in AdS

We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in $AdS_3$. The solutions are expressed in terms of the generating function for the products of Bell polynomials in derivatives of bosonic space-time coordinates $X^m(z)$ of the open string, which form is determined in this work. The products of these polynomials form a natural operator algebra realizations of $W_\infty$ (area-preserving diffeomorphisms), enveloping algebra of SU(2) and higher spin algebra in $AdS_3$. The class of SFT solutions found can, in turn, be interpreted as the "enveloping of enveloping", or the enveloping of $AdS_3$ higher spin algebra. We also discuss the extensions of this class of solutions to superstring theory and their relations to higher spin algebras in higher space-time dimensions.

hep-th↗

arXiv2015

Non-commutativity from the double sigma model

We show how non-commutativity arises from commutativity in the double sigma model. We demonstrate that this model is intrinsically non-commutative by calculating the propagators. In the simplest phase configuration, there are two dual copies of commutative theories. In general rotated frames, one gets a non-commutative theory and a commutative partner. Thus a non-vanishing $B$ also leads to a commutative theory. Our results imply that $O\left(D,D\right)$ symmetry unifies not only the big and small torus physics, but also the commutative and non-commutative theories. The physical interpretations of the metric and other parameters in the double sigma model are completely dictated by the boundary conditions. The open-closed relation is also an $O(D,D)$ rotation and naturally leads to the Seiberg-Witten map. Moreover, after applying a second dual rotation, we identify the description parameter in the Seiberg-Witten map as an $O(D,D)$ group parameter and all theories are non-commutative under this composite rotation. As a bonus, the propagators of general frames in double sigma model for open string are also presented.

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arXiv2014

New analytic solutions in String Field Theory: towards collective Higher Spin vacuum

We construct analytic solutions in cubic open superstring field theory at higher superconformal ghost numbers.The solutions are the pure ghost ones and are given by combinations of Bell polynomials of bosonized superconformal ghost fields multiplied by exponents of the bosonized ghosts. Based on the structure of the solutions, we conjecture them to describe the ghost part of collective vacuum for higher spin modes in open string theory.

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arXiv2013

String Theory and Emergent AdS Geometry in Higher Spin Field Theories

We analyze the Weyl invariance constraints on higher spin vertex operators in open superstring theory describing massless higher spin gauge field excitations in d-dimensional space-time. We show that these constraints lead to low-energy equations of motion for higher spin fields in AdS space, with the leading order beta-function for the higher spin fields producing Fronsdal's operator in $AdS_{d+1}$, despite that the higher spin vertex operators are originally defined in flat background. The correspondence between the $\beta$-function in string theory and $AdS_{d+1}$ Fronsdal operators in space-time is found to be exact for $d=4$, while for other space-time dimensions it requires modifications of manifest expressions for the higher spin vertex operators. We argue that the correspondence considered in this paper is the leading order of more general isomorphism between Vasiliev's equations and equations of motion of extended open string field theory (OSFT), generalized to include the higher spin operators.

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arXiv2013

Higher Spin Contributions to Holographic Fluid Dynamics in $AdS_5/CFT_4$

We calculate the graviton's $\beta$-function in $AdS$ string-theoretic sigma-model, perturbed by vertex operators for Vasiliev's higher spin gauge fields in $AdS_5$. The result is given by $\beta_{mn}=R_{mn}+4T_{mn}(g,u)$ (with the AdS radius set to 1 and the graviton polarized along the $AdS_5$ boundary), with the matter stress-energy tensor given by that of conformal holographic fluid in $d=4$, evaluated at the temperature given by $T={1\over{\pi}}$. The stress-energy tensor is given by $T_{mn}={g_{mn}}+4u_mu_n+\sum_{N}T^{(N)}_{mn}$ where $u$ is the vector excitation satisfying $u^2=-1$ and $N$ is the order of the gradient expansion in the dissipative part of the tensor. We calculate the contributions up to N=2. The higher spin excitations contribute to the $\beta$-function, ensuring the overall Weyl covariance of the matter stress tensor. We conjecture that the structure of gradient expansion in $d=4$ conformal hydrodynamics at higher orders is controlled by the higher spin operator algebra in $AdS_5$.

hep-th↗

arXiv2012

Higher Spin Holography and AdS String Sigma-Model

We analyze cubic spin 3 interaction in AdS space using the higher spin extension of string-theoretic sigma-model constructed in our previous work, which low energy limit is described by AdS vacuum. We find that, in the leading order of the cosmological constant, the spin 3 correlator on the AdS4 string theory side reproduces the structure of 3 point function of composite operators, quadratic in free fields, in the dual vector model. The cancellation of terms violating higher spin holography is related to the value of the Liouville background charge in four dimensions.

hep-th↗

arXiv2012

String Amplitudes and Frame-like Formalism for Higher Spins

We analyze open string vertex operators describing connection gauge fields for spin 3 in Vasiliev's frame-like formalism and perform their extended BRST analysis. Gauge symmetry transformations, generalized zero torsion constraints relating extra fields to the dynamical frame-like field and relation between dynamical frame-like field and fully symmetric Fronsdal's field for spin 3 are all realized in terms of BRST constraints on these vertex operators in string theory. Using the construction, we analyze the 3-point correlator for spin 3 field and calculate Chern-Simons type cubic interactions described by 3-derivative Berends-Burgers-van Dam (BBD) type vertex in the frame-like formalism.

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