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Register a new userExact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5
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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.
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We study a general class of spinning pulsating strings in $(AdS_5 times S^5)_{varkappa}$ background. For these family of solitons, we examine the scaling relation between the energy, spin or angular momentum. We verify that in $varkappa rightarrow 0 $ limit these relations reduce to the undeformed $AdS_5 times S^5$ case. We further study an example of a string which is spinning in the $varkappa$-deformed AdS$_5$ and S$^5$ simultaneously and find out the scaling relation among various conserved charges.
We revisit the computation of the 1-loop string correction to the latitude minimal surface in $AdS_5 times S^5$ representing 1/4 BPS Wilson loop in planar $cal N$=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the $AdS_2$ minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on $AdS_2$. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and $k$-wound circle.
We consider a computation of one-loop AdS_5 x S^5 superstring correction to the energy radiated by the end-point of a string which moves along a wavy line at the boundary of AdS_5 with a small transverse acceleration (the corresponding classical solution was described by Mikhailov in hep-th/0305196). We also compute the one-loop effective action for an arbitrary small transverse string fluctuation background. It is related by an analytic continuation to the Euclidean effective action describing one-loop correction to the expectation value of a wavy Wilson line. We show that both the one-loop contribution to the energy and to the Wilson line are controlled by the subleading term in the strong-coupling expansion of the function B(lambda) as suggested by Correa, Henn, Maldacena and Sever in arXiv:1202.4455.
We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on two parameters: a single S^5 angular momentum J and the string tension lambda. In the general case both parameters can be finite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with lambda=lambda/J^2 fixed recovers the plane-wave Hamiltonian and higher-order corrections recently studied in the literature. In the strong coupling limit lambdato infty, J fixed, the energy of short strings scales as sqrt[4]{lambda} while the energy of long strings scales as sqrt{lambda}. We further show that the gauge-fixed Hamiltonian is integrable by constructing the corresponding Lax representation. We discuss some general properties of the monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum perfectly agrees with the one obtained earlier for some specific cases.
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.
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