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Register a new userStatic Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
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Motivated by the notorious difficulties in determining the first quantum corrections to the spectrum of short strings in AdS_5xS^5 from first principles, we study closed bosonic strings in this background employing a static gauge. In this gauge the world-sheet Hamiltonian density is constant along the extension of the string and directly proportional to the square of the spacetime energy. We quantize this system in a minisuperspace approach, in which we consider only a single AdS_5 string mode excitation next to an arbitrary particle like zero-mode contribution in the full AdS_5xS^5 background. We determine the quantum spectrum using this method to the next-to-next-to-leading order in the large t Hooft coupling expansion. We argue for an ordering prescription which should arise from supersymmetrization and indeed recover the integrability based predictions for the spectrum of the lightest excitation, dual to the Konishi field scaling dimensions. The higher excitations fail to agree, but this is shown to be a consequence of the string mode truncation employed. Despite this simple setup, our system reveals intriguing features, such as a close connection to particles in AdS_6, classical integrability and preservation of the isometries of AdS_5xS^5 at the quantum level.
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We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS_5xS^5. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop N=4 supersymmetric gauge theory proving the complete agreement of spectra in this approximation.
Using information from the marginality conditions of vertex operators for the AdS_5 x S^5 superstring, we determine the structure of the dependence of the energy of quantum string states on their conserved charges and the string tension proportional to lambda^(1/2). We consider states on the leading Regge trajectory in the flat space limit which carry one or two (equal) spins in AdS_5 or S^5 and an orbital momentum in S^5, with Konishi multiplet states being particular cases. We argue that the coefficients in the energy may be found by using a semiclassical expansion. By analyzing the examples of folded spinning strings in AdS_5 and S^5 as well as three cases of circular two-spin strings we demonstrate the universality of transcendental (zeta-function) parts of few leading coefficients. We also show the consistency with target space supersymmetry with different states belonging to the same multiplet having the same non-trivial part of the energy. We suggest, in particular, that a rational coefficient (found by Basso for the folded string using Bethe Ansatz considerations and which, in general, is yet to be determined by a direct two-loop string calculation) should, in fact, be universal.
Previous attempts to match the exact N=4 super Yang-Mills expression for the expectation value of the 1/2-BPS circular Wilson loop with the semiclassical AdS(5)xS(5) string theory prediction were not successful at the first subleading order. There was a missing prefactor ~ lambda^(-3/4) which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1/4-supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes of the transverse fluctuation operator in the 5-sphere directions.
In the present paper, which is a sequel to arXiv:1001:4018, we compute the one-loop correction to the energy of pulsating string solutions in AdS_5 x S^5. We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can be also put into the single-gap Lame form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the short string limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of small semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.
Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory for the longitudinal variables X^{pm}, psi^{pm}. We show that with the transverse variables and the ghosts combined, it is possible to construct a nilpotent BRST charge.
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