arXiv subjects

Sergey Frolov

Publications and source records attributed to Sergey Frolov.

59 records · Page 4Linked to original sources

arXiv2005

Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector

We introduce a uniform light-cone gauge for strings propagating in AdS space-time. We use the gauge to analyze strings from the su(1|1) sector, and show that the reduced model is described by a quadratic action for two complex fermions. Thus, the uniform light-cone gauge allows us to solve the model exactly. We analyze the near BMN spectrum of states from the su(1|1) sector and show that it correctly reproduces the 1/J corrections. We also compute the spectrum in the strong coupling limit, and derive the famous λ^{1/4} asymptotics. We then show that the same string spectrum can be also derived by solving Bethe ansatz type equations, and discuss their relation to the quantum string Bethe ansatz for the su(1|1) sector.

hep-th↗

arXiv2005

Lax Pair for Strings in Lunin-Maldacena Background

Recently Lunin and Maldacena used an SL(3,R) transformation of the AdS_5 x S^5 background to generate a supergravity solution dual to a so-called beta-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the beta-deformed background for real beta, and show that solutions of string theory equations of motion in this background are in one-to-one correspondence with those in AdS_5 x S^5 with twisted boundary conditions imposed on the U(1) isometry fields. We then apply the TsT transformation to derive a local and periodic Lax pair for the bosonic part of string theory in the beta-deformed background. We also perform a chain of three consecutive TsT transformations to generate a three-parameter deformation of AdS_5 x S^5. The three-parameter background is dual to a nonsupersymmetric marginal deformation of N=4 SYM. Finally, we combine the TsT transformations with SL(2,R) ones to obtain a 6+2 parameter deformation of AdS_5 x S^5.

hep-th↗

arXiv2004

Bethe Ansatz for Quantum Strings

We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of arbitrary M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M=2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 (n^2 lambda)^(1/4) asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

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arXiv2001

String Corrections to the Holographic RG Flow of Supersymmetric SU(N) x SU(N+M) Gauge Theory

We study leading string corrections to the type IIB supergravity solution dual to the ${\cal N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory coupled to bifundamental chiral superfields $A_i, B_j$, $i,j=1,2$. This solution was found in hep-th/0007191, and its asymptotic form describing logarithmic RG flow was constructed in hep-th/0002159. The leading tree-level string correction to the type IIB string effective action is represented by the invariant of the form $\a'{}^3 (R^4 + ...)$. Since the background contains 3-form field strengths, we need to know parts of this invariant that depend on them. By analyzing the 5-point superstring scattering amplitudes we show that only a few specific $R^3 (H_3)^2$ and $R^3 (F_3)^2$ terms are present in the effective action. Their contribution to the holographic RG flow turns out to be of the same order as of the $R^4$ terms. Using this fact we show that it is possible to have agreement between the $α'$-corrected radial dependence of the supergravity fields and the RG flow dictated by the NSVZ beta functions in field theory. The agreement with field theory requires that the anomalous dimension of the operators $\Tr (A_i B_j)$ is corrected by a term of order $(M/N)^4 λ^{-1/2}$ from its value $-{1 \over 2} $ found for M=0 ($λ$ is the appropriate 't Hooft coupling which is assumed to be strong).

hep-th↗

arXiv2001

On off-shell structure of open string sigma model

We analyze several problems related to off-shell structure of open string sigma model by using a combination of derivative expansion and expansion in powers of the fields. According to the sigma model approach to bosonic open string theory, the tachyon effective action $S(T)$ coincides with the renormalized partition function $Z(T)$ of sigma model on a disk, up to a term vanishing on shell. On the other hand, $Z(T)$ is a generating functional of perturbative open string scattering amplitudes. If $S(T) = Z(T)$, then there should be no contribution of exchange diagrams to string amplitudes computed using $S(T)$. We compute the cubic term in the effective action, and show that it vanishes if some but not all external legs are on shell, and, therefore, any exchange diagram involving the cubic term vanishes too. Then, we discuss a problem of turning on nonrenormalizable boundary interactions, corresponding to massive string modes. We compute the quadratic term for a symmetric tensor field, and show that despite nonrenormalizability of the model one can consistently remove all divergent terms, and obtain a quadratic action reproducing the on-shell condition for the field. We also briefly discuss fermionic (NS) sigma model, compute the tachyon quadratic term, and show that it reproduces the correct tachyon mass. We note that turning on a massive symmetric tensor field leads to the appearance of a term linear in it, which can be removed by adding a higher-derivative term to the boundary of the disc.

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