arXiv subjects

Dimitri Polyakov

Publications and source records attributed to Dimitri Polyakov.

At least 37 records · Page 2Linked to original sources

arXiv2011

A String Model for AdS Gravity and Higher Spins

We construct a string sigma-model which low energy limit describes the anti de Sitter gravity and spin 3 massless fields in Vasiliev's frame-like formalism. The model is based on vertex operators generating vielbein and connection fields in the Mac Dowell - Mansoury - Stelle - West (MMSW) formulation of gravity. The structure of the vertex operators is based on the hidden symmetry generators in RNS superstring theory, realizing the isometry group of the AdS space. The beta-function equations in the sigma-model lead to equations of motion in the MMSW gravity with negative cosmological constant with the AdS geometry being the vacuum solution. Generalizations for the higher spin fields are analyzed and equations of motion for spin 3 fields in $d=3$ in frame-like formalism are obtained in the low energy limit of string theory. These equations correspond to those of $sl(3,R)$ truncated Chern-Simons action based on higher spin algebra $hs(1,1)$.

hep-th↗

arXiv2010

Higher Spins and Open Strings: Quartic Interactions

We analyze quartic gauge-invariant interactions of massless higher spin fields by using vertex operators constructed in our previous works and computing their four-point amplitudes in superstring theory. The kinematic part of the quartic interactions of the higher spins is determined by the matter structure of their vertex operators;the non-locality of the interactions is the consequence of specific ghost structure of these operators. We compute explicitly the four-point amplitude describing the complete gauge-invariant $1-1-3-3$ quartic interaction (two massless spin 3 particles interacting with two photons) and comment on more general $1-1-s-s$ cases, particularly pointing out the structure of $1-1-5-5$ coupling.

hep-th↗

arXiv2010

Gravitational Couplings of Higher Spins from String Theory

We calculate the interaction 3-vertex of two massless spin 3 particles with a graviton using vertex operators for spin 3 fields in open string theory, constructed in our previous work. The massless spin 3 fields are shown to interact with the graviton through the linearized Weyl tensor, reproducing the result by Boulanger, Leclercq and Sundell. This is consistent with the general structure of the non-Abelian $2-s-s$ couplings, implying that the minimal number of space-time derivatives in the interaction vertices of two spin s and one spin 2 particle is equal to $2s-2$.

hep-th↗

arXiv2009

Interactions of Massless Higher Spin Fields From String Theory

We construct vertex operators for massless higher spin fields in RNS superstring theory and compute some of their three-point correlators, describing gauge-invariant cubic interactions of the massless higher spins. The Fierz-Pauli on-shell conditions for the higher spins (including tracelessness and vanishing divergence) follow from the BRST-invariance conditions for the vertex operators constructed in this paper. The gauge symmetries of the massless higher spins emerge as a result of the BRST nontriviality conditions for these operators, being equivalent to transformations with the traceless gauge parameter in the Fronsdal's approach. The gauge invariance of the interaction terms of the higher spins is therefore ensured automatically by that of the vertex operators in string theory. We develop general algorithm to compute the cubic interactions of the massless higher spins and use it to explicitly describe the gauge-invariant interaction of two $s=3$ and one $s=4$ massless particles.

hep-th↗

arXiv2009

New BRST Charges in RNS Superstring Theory and deformed Pure Spinors

We show that new BRST charges in RNS superstring theory with nonstandard ghost numbers, constructed in our recent work, can be mapped to deformed pure spinor (PS) superstring theories, with the nilpotent pure spinor BRST charge $Q_{PS}=\oint{λ^α}d_α$ still retaining its form but with singular operator products between commuting spinor variables $λ^α$. Despite the OPE singularities, the pure spinor condition $λγ^mλ=0$ is still fulfilled in a weak sense, explained in the paper. The operator product singularities correspond to introducing interactions between the pure spinors. We conjecture that the leading singularity orders of the OPE between two interacting pure spinors is related to the ghost number of the corresponding BRST operator in RNS formalism. Namely, it is conjectured that the BRST operators of minimal superconformal ghost numbers $n=1,2,3...$ can be mapped to nilpotent BRST operators in the deformed pure spinor formalism with the OPE of two commuting spinors having a leading singularity order $λ(z)λ(w)\sim{O}(z-w)^{-2(n^2+6n+1)}$. The conjecture is checked explicitly for the first non-trivial case $n=1$.

hep-th↗

arXiv2009

Ground Ring of Alpha-Symmetries and Sequence of RNS String Theories

We construct a sequence of nilpotent BRST charges in RNS superstring theory, based on new gauge symmetries on the worldsheet, found in this paper. These new local gauge symmetries originate from the global nonlinear space-time $α$-symmetries, shown to form a noncommutative ground ring in this work. The important subalgebra of these symmetries is $U(3)\times{X_6}$, where $X_6$ is solvable Lie algebra consisting of 6 elements with commutators reminiscent of the Virasoro type. We argue that the new BRST charges found in this work describe the kinetic terms in string field theories around curved backgrounds of the $AdS\times{CP}_n$-type, determined by the geometries of hidden extra dimensions induced by the global $α$-generators. The identification of these backgrounds is however left for the work in progress.

hep-th↗

arXiv2009

Noncommutativity and Ramond-Ramond fields

We study the properties of the Ramond fields in superstring theory in the presence of a constant B-field and the subsequent implications of space-time noncommutativity for space-time fermions and space-time supersymmetry. We find that the noncommutativity of space-time coordinates leads to extra singularities in the spin field correlators and to appearance of the extra poles in the RR scattering amplitudes, carrying the opposite GSO parities.

hep-th↗

arXiv2008

(Non)triviality of Pure Spinors and Exact Pure Spinor - RNS Map

All the BRST-invariant operators in pure spinor formalism in $d=10$ can be represented as BRST commutators, such as $V=\lbrace{Q_{brst}},{θ_{+}\over{λ_{+}}}V\rbrace$ where $λ_{+}$ is the U(5) component of the pure spinor transforming as $1_{5\over2}$. Therefore, in order to secure non-triviality of BRST cohomology in pure spinor string theory, one has to introduce "small Hilbert space" and "small operator algebra" for pure spinors, analogous to those existing in RNS formalism. As any invariant vertex operator in RNS string theory can also represented as a commutator $V=\lbrace{Q_{brst}},LV\rbrace$ where $L=-4c\partialξξe^{-2ϕ}$, we show that mapping ${θ_{+}\over{λ_{+}}}$ to L leads to identification of the pure spinor variable $λ^α$ in terms of RNS variables without any additional non-minimal fields. We construct the RNS operator satisfying all the properties of $λ^α$ and show that the pure spinor BRST operator $\oint{λ^α{d_α}}$ is mapped (up to similarity transformation) to the BRST operator of RNS theory under such a construction. We also observe that BRST cohomology of pure spinor superstring theory contains vertex operators non-trivially coupled to the pure spinor ghost variable. The physical interpretation of these operators remains unclear.

hep-th↗

arXiv2008

$α$-Symmetries, Coloured Dimensions and Gauge-String Correspondence

We propose a scenario of gauge-string correspondence by relating the SU(3) colour group to hidden space-time isometries originating from extra dimensions. These isometries ($α$-symmetries) are the special symmetries of RNS superstring theories under global non-linear space-time transformations. The vertex operators for the octet of gluons are constructed by the procedure of ``photon painting'', that is, with the SU(3) subgroup of the $α$-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator algebra of these massless gluon vertices is closed and possesses the full zigzag symmetry, crucial for the isomorphism between open strings and QCD. As a result, the scattering amplitudes of the constructed open string vertex operators have a field-theoretic rather than a stringy structure, including the absense of standard tower of massive intermediate states.Our model also suggests that the total number of underlying hidden dimensions is three, with each extra dimension carrying its appropriate SU(3) colour and anticolour.

hep-th↗

arXiv2007

New Superstring Isometries and Hidden Dimensions

We explore the hierarchy of hidden space-time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is cancelled by that of the ghost part. These symmetries, referred to as the $α$-symmetries, are induced by special space-time generators, violating the equivalence of ghost pictures. We classify the $α$-symmetry generators in terms of superconformal ghost cohomologies $H_{n}\sim{H_{-n-2}}(n\geq{0})$ and associate these generators with a chain of hidden space-time dimensions, with each ghost cohomology $H_{n}\sim{H_{-n-2}}$ ``contributing'' an extra dimension. Namely, we show that each ghost cohomology $H_{n}\sim{H_{-n-2}}$ of non-critical superstring theory in $d$-dimensions contains $d+n+1$ $α$-symmetry generators and the generators from $H_{k}\sim{H_{-k-2}},1\leq{k}\leq{n}$, combined together, extend the space-time isometry group from the naive $SO(d,2)$ to $SO(d+n,2)$. In the simplest case of $n=1$ the $α$-generators are identified with the extra symmetries of the $2T$-physics formalism, also known to originate from a hidden space-time dimension.

hep-th↗

arXiv2007

Ghost Cohomologies and Hidden Space-Time Symmetries

We observe and study new non-linear global space-time symmetries of the full ghost+matter action of RNS superstring theory. We show that these surprising new symmetries are generated by the special worldsheet currents (vertex operators) of RNS superstring theory, violating the equivalence of superconformal ghost pictures. We review the questions of BRST invariance and non-triviality of picture-dependent vertex operators and show their relation to hidden space-time symmetries and hidden space-time dimensions. In particular, we relate the space-time transformations, induced by the picture-dependent currents, to the symmetries observed in the 2T physics approach.

hep-th↗

arXiv2006

New Discrete States in Two-Dimensional Supergravity

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra.Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. We show that the interaction of $d=2$ superstrings with the superconformal ghosts enlarges the algebra of dimension 1 currents and hence the new discrete states appear. These new states are the SU(N) multiplets, if the algebra includes the currents of ghost numbers from -N to N-2, not related by the picture-changing. We compute the structure constants of these new discrete states for N=3 and express them in terms of SU(3) Clebsch-Gordan coefficients,relating their operator algebra to the volume preserving diffeomorphisms in d=3. For general N, the algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between 2d superstrings and field theories in higher dimensions.

hep-th↗

arXiv2005

GL(1) Charged States in Twistor String Theory

We discuss the appearance of the GL(1) charged physical operators in the twistor string theory. These operators are shown to be BRST-invariant and non-trivial, and some of their correlators and conformal beta-functions are computed. Remarkably, the non-conservation of the GL(1)-charge in interactions involving these operators is related to the anomalous term in the Kac-Moody current algebra. While these operators play no role in the maximum helicity violating (MHV) amplitudes of Yang-Mills theory, they are shown to contribute non-trivially to non-MHV correlators in the worldsheet instanton backgrounds. We argue that these operators describe the non-perturbative dynamics of solitons in conformal supergravity. However, the exact form of such solitonic solutions is yet to be determined.

hep-th↗

arXiv2005

Conformal Moduli and b-c Pictures for NSR Strings

We explore the geometry of the superconformal moduli of the NSR superstring theory in order to construct the consistent sigma-model for the NSR strings, free of picture-changing ambiguities. The sigma-model generating functional is constructed by the integration over the bosonic and anticommuting moduli, corresponding to insertions of the vertex operators in scattering amplitudes. In particular, the integration over the bosonic moduli results in the appearance of picture-changing operators for the b-c system. Important example of the b-c pictures involves the unintegrated and integrated forms of the vertex operators. We derive the BRST-invariant expressions for the b-c picture-changing operators for open and closed strings and study some of their properties. We also show that the superconformal moduli spaces of the NSR superstring theory contain the global singularities, leading to the appearance of non-perturbative solitonic D-brane creation operators.

hep-th↗

arXiv2004

Fluid Dynamics of NSR Strings

We show that the renormalization group flows of the massless superstring modes in the presence of fluctuating D-branes satisfy the equations of fluid dynamics.In particular, we show that the D-brane's U(1) field is related to the velocity function in the Navier-Stokes equation while the dilaton plays the role of the passive scalar advected by the turbulent flow. This leads us to suggest a possible isomorphism between the off-shell superstring theory in the presence of fluctuating branes and the fluid mechanical degrees of freedom.

hep-th↗

arXiv2003

Ghost-Matter Mixing and Feigenbaum Universality in String Theory

Brane-like vertex operators, defining backgrounds with the ghost-matter mixing in NSR superstring theory, play an important role in a world-sheet formulation of D-branes and M theory, being creation operators for extended objects in the second quantized formalism. In this paper we show that dilaton's beta function in ghost-matter mixing backgrounds becomes stochastic. The renormalization group (RG) equations in ghost-matter mixing backgrounds lead to non-Markovian Fokker-Planck equations which solutions describe superstrings in curved space-times with brane-like metrics.We show that Feigenbaum universality constant $δ=4,669...$ describing transitions from order to chaos in a huge variety of dynamical systems, appears analytically in these RG equations. We find that the appearance of this constant is related to the scaling of relative space-time curvatures at fixed points of the RG flow. In this picture the fixed points correspond to the period doubling of Feigenbaum iterational schemes.

hep-th↗

arXiv2002

DBI Action from Closed Strings and D-brane second Quantization

Brane-like vertex operators play an important role in a worldsheet formulation of D-branes and M-theory. In this paper we derive the DBI D-brane action from NSR closed string sigma-model with brane-like states. We also show that these operators carry RR charges and define D-brane wavefunctions in a second quantized formalism.

hep-th↗

arXiv2002

On Noncommutativity in String Theory and D-Branes

By considering the B-field dynamical and studying its interaction with Ramond-Ramond (RR) background we observe the breaking of the B-field gauge symmetry in the effective action. This effect takes place due to non-perturbative coupling of the B-field to membrane topological charge. As a result, the B-field is renormalized in the RR backgrounds, making it impossible to obtain consistent non-commutative models with constant B-field. We argue that the gauge invariance is restored by introducing appropriate external D-brane configuration.

hep-th↗