No Arabic abstract
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.
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.
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 study non-planar correlators in ${cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 times S^5$ in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.
We consider $alpha$ corrections to the one-loop four-point correlator of the stress-tensor multiplet in $mathcal{N}=4$ super Yang-Mills at order $1/N^4$. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS$_5times$S$^5$. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop-amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in $alpha$ not considered before.
We provide a formalism to calculate the cubic interaction vertices of the stable string bit model, in which string bits have $s$ spin degrees of freedom but no space to move. With the vertices, we obtain a formula for one-loop self-energy, i.e., the $mathcal{O}left(1/N^{2}right)$ correction to the energy spectrum. A rough analysis shows that, when the bit number $M$ is large, the ground state one-loop self-energy $Delta E_{G}$ scale as $M^{5-s/4}$ for even $s$ and $M^{4-s/4}$ for odd $s$. Particularly, in $s=24$, we have $Delta E_{G}sim 1/M$, which resembles the Poincare invariant relation $P^{-}sim 1/P^{+}$ in $(1+1)$ dimensions. We calculate analytically the one-loop correction for the ground energies with $M=3$ and $s=1,,2$. We then numerically confirm that the large $M$ behavior holds for $sleq4$ cases.