Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPrecision calculation of 1/4-BPS Wilson loops in AdS$_5times S^5$
77
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of latitudes) in ${cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5times$S$^5$. Supersymmetric localization provides an exact result that, in the large t Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the $ratio$ between the generic latitude and the maximal 1/2-BPS circle: Any measure-related ambiguity should simply cancel in this way. We use Gelfand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: The difference is encoded into a precise remainder function. We comment on the possible origin and resolution of this discordance.
rate research
Read More
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.
We proceed to study Yang-Baxter deformations of the AdS$_5times$S$^5$ superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present the master formula to describe the dilaton in terms of classical $r$-matrices. The supercoset construction is explicitly performed for some classical $r$-matrices and the full backgrounds including the Ramond-Ramond (R-R) sector and dilaton are derived. Within the class of abelian $r$-matrices, the perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theories, $gamma$-deformations of S$^5$ and Schrodinger spacetimes. It would be remarkable that the supercoset construction works well, even if the resulting backgrounds are not maximally supersymmetric. In particular, three-parameter $gamma$-deformations of S$^5$ and Schrodinger spacetimes do not preserve any supersymmetries. As for non-abelian $r$-matrices, we will focus upon a specific example. The resulting background does not satisfy the equation of motion of the Neveu-Schwarz-Neveu-Schwarz (NS-NS) two-form because the R-R three-form is not closed.
Three dimensional supersymmetric field theories have large moduli spaces of circular Wilson loops preserving a fixed set of supercharges. We simplify previous constructions of such Wilson loops and amend and clarify their classification. For a generic quiver gauge theory we identify the moduli space as a quotient of $C^m$ for some $m$ by an appropriate symmetry group. These spaces are quiver varieties associated to a cover of the original quiver or a subquiver thereof. This moduli space is generically singular and at the singularities there are large degeneracies of operators which seem different, but whose expectation values and correlation functions with all other gauge invariant operators are identical. The formulation presented here, where the Wilson loops are on $S^3$ or squashed $S^3_b$ also allows to directly implement a localization procedure on these observables, which previously required an indirect cohomological equivalence argument.
The genus zero contribution to the four-point correlator $langle {cal O}_{p_1}{cal O}_{p_2}{cal O}_{p_3}{cal O}_{p_4}rangle$ of half-BPS single-particle operators ${cal O}_p$ in $mathcal{N}=4$ super Yang-Mills at strong coupling computes the Virasoro-Shapiro amplitude of closed superstrings on $AdS_5times S^5$. Combining Mellin space techniques, the large $p$ limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its $alpha$ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large $p$ limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the $alpha$ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in $AdS_5times S^5$ up to a small number of ambiguities at each order and we compute it explicitly for $(alpha)^{5,6,7,8,9}$. As the order of $alpha$ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions. This correction is uniquely determined and lifts the residual degeneracy of tree level supergravity due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in $alpha$.It is analytic in the quantum numbers, symmetric under an $AdS_5 leftrightarrow S^5$ exchange, and it enjoys intriguing properties, which we explain and detail in various cases.
In this paper we study spin 2 fluctuations around a warped $AdS_3 times S^2 times T^4 times mathcal{I}_{rho}$ background in type IIA supergravity with small $mathcal{N} = (0,4)$ supersymmetry. We find a class of fluctuations, which will be called textit{universal}, that is independent of the background data and corresponds to operators with scaling dimension $Delta = 2l +2$, being $l$ the angular-momentum-quantum-number on the $S^2$ which realises the $SU(2)_R$ symmetry. We compute the central charge for $mathcal{N} = (0,4)$ two-dimensional superconformal theories from the action of the spin 2 fluctuations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
