Luscher Term for k-string Potential from Holographic One Loop Corrections
Leopoldo A. Pando Zayas, Vincent G. J. Rodgers, Kory Stiffler
备注：
39 pages, 3 figures. New Calculation showing explicit k -> M - k symmetry of Energy utilizing the new figure. Discussion of non-k-dependence of Luscher term at end of last section right before Conclusion. Same version to be published in JHEP
We perform a systematic analysis of k-strings in the framework of the gauge/gravity correspondence. We discuss the Klebanov-Strassler supergravity background which is known to be dual to a confining supersymmetric gauge theory with chiral symmetry breaking. We obtain the k-string tension in agreement with expectations of field theory. Our main new result is the study of one-loop corrections on the string theoretic side. We explicitly find the frequency spectrum for both the bosons and the fermions for quadratic fluctuations about the classical supergravity solution. Further we use the massless modes to compute 1/L contributions to the one loop corrections to the k-string energy. This corresponds to the Luscher term contribution to the k-string potential on the gauge theoretic side of the correspondence.
The leading term for the energy of a bound state of k-quarks and k-antiquarks is proportional to its separation L. These k-string configurations have a Luscher term associated with their quantum fluctuations which is typically a 1/L correction to the energy. We review the status of tensions and Luscher terms in the context of lattice gauge theory, Hamiltonian methods, and gauge/gravity correspondence. Furthermore we explore how different representations of the k-string manifest themselves in the gauge/gravity duality. We calculate the Luscher term for a strongly coupled SU(N) gauge theory in (…
In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in AdS3, as we demonstrate here by studying Luscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernandez & Lopez, in which the su(2) sector Bethe equations (including one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations did not agree in AdS3xS3xT4, and we show that the sum of all massless Luscher F-terms can reproduce the di…
We calculate the Luscher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian subgroup. The Luscher term is determined by the number of light degrees of freedom on the string wordsheet. Unlike the standard π/12 we get Nπ/12 for non-Abelian strings in the U(N) gauge theories. Thus, the Luscher coefficient acquires a dependence on the rank of the gauge group. In the models with non-Abelian strings discussed in the literature there are …
In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on t…
We analyze the holographic description of several properties of $\N=1$ confining gauge dynamics. In particular we discuss Wilson loops including the issues of a Luscher term and the broadening of the flux tubes, 't Hooft loops, baryons, instantons, chiral symmetry breaking, the gluino condensate and BPS domain walls.
We compute classical and first quantum finite-size corrections to the recently found giant magnon solutions in two different subspaces of $\mathbb{CP}^3$. We use the Lüscher approach on the recently proposed exact S-matrix for $\mathcal{N}=6$ superconformal Chern-Simons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a non-trivial test for the new $AdS_4/CFT_3$ correspondence within an integrability framework.
A brief historical synopsis of the connection between gauge theories and string theory is given. Meson configurations known as k-strings are examined from string theory via the gauge/gravity correspondence. Backgrounds dual to k-strings in both 2+1 and 3+1 are discussed. The energy of k-strings to lowest order consists of a tension term, proportional to the length, L, of the k-string, i.e., the size of the mesons in the configuration. The first quantum correction is a Coulombic 1/L correction, known as a Luscher term, plus a constant. Acquiring tensions and Luscher terms via the gauge/gravity …
We derive the perturbative four loop anomalous dimension of the Konishi operator in N=4 SYM theory from the integrable string sigma model by evaluating the finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. We obtain these multiparticle generalizations of Luscher formulas by studying certain exactly solvable relativistic integrable quantum field theories. The final result involves a summation of all bound states in the mirror theory and agrees with gauge theory perturbative computations.
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Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put toward this goal. A set of specific tools which are used in this effort are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dp-branes embedded in confining supergravity backgrounds from low energy superstring field theory. Along …
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We calculate the energy spectrum of closed strings in SU(N) gauge theories with N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control all systematic errors, and this allows us to perform a precise comparison with different theoretical predictions. When we study the dependence of the string mass on its length L we find that the Nambu-Goto prediction is a very good approximation down to relatively short lengths, where the Luscher term alone is insufficient. We then isolate the corrections to the Luscher term, and compare them to recent theoretical predictions, which indeed seem…
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In this review article we present the calculation of the splitting rate in flat space of a macroscopic fundamental string either intersecting at a generic angle a Dp-brane or lying on it. The result is then applied, in the context of the string/gauge theory correspondence, to the study of exclusive decay rates of large spin mesons into mesons. As examples, we discuss the cases of N=4 SYM with a small number of flavors, and of QCD-like theories in the quenched approximation. In the latter context, explicit analytic formulas are given for decay rates of mesons formed either by heavy quarks or by…
We study the behaviour of the interquark potential in lattice gauge theories at high temperature, but still in the confining phase, and propose a new observable which could play in this regime the same role played by the Luscher term in the low temperature limit. This quantity is related to the exponent of the power prefactor in the effective string partition function or, equivalently, to the coefficient of the logarithmic correction in the interquark potential and, as for the usual Luscher term, its value does not depend on the particular gauge group under consideration or on the form of the …
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We study the emergence of partonic behavior in scattering processes at large Mandelstam's variable $s$ from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler (2001) in two ways. (i) We analyze several holographic confining backgrounds in particular the hard wall model, the soft wall model and Witten's model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to …
To understand the time-dependent quantum correlation in expanding universes, we study the time-dependent entanglement entropy in the braneworld model. If we take into account a generalized string cloud geometry caused by uniformly distributed open strings, cosmologies on the braneworld result in the standard Friedmann-Lemaître-Robertson-Walker cosmologies with various matter contents. On the dual field theory side, open strings are reinterpreted as a fundamental matter, while the black hole mass corresponds to the excitation energy of massless gauge bosons. In this work, we show how the string…
We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in semi-classical way and to compute the corrections to the string energies. These results are compared with the F-term Lüscher formula based on the S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly provides another stringent test for the all-loop integrability conjecture and the exact S-matrix based on it.
There has been considerable recent interest in holographic complexity. The two leading conjectures on this subject hold that the quantum complexity of the boundary thermofield double state should be dual to either the volume of the Einstein-Rosen bridge connecting the two sides (CV conjecture) or to the action of the Wheeler-de-Witt patch of the bulk spacetime (CA conjecture). Although these conjectures are frequently studied in the context of pure Einstein gravity, from the perspective of string theory it is also natural to consider models of gravity in which general relativity is perturbed b…
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We investigate the dispersion relation of the winding closed-string states in SU(N) gauge theory defined on a d-dimensional hypertorus, in a class of effective string theories. We show that order by order in the asymptotic expansion, each energy eigenstate satisfies a relativistic dispersion relation. This is illustrated in the Luscher-Weisz effective string theory to two-loop order, where the Polyakov loop matrix elements between the vacuum and the closed string states are obtained explicitly. We attempt a generalization of these considerations to the case of compact dimensions transverse to …
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Products of large-N conformal field theories coupled by multi-trace interactions in diverse dimensions are used to define quantum multi-gravity (multi-string theory) on a union of (asymptotically) AdS spaces. One-loop effects generate a small O(1/N) mass for some of the gravitons. The boundary gauge theory and the AdS/CFT correspondence are used as guiding principles to study and draw conclusions on some of the well known problems of massive gravity - classical instabilities and strong coupling effects. We find examples of stable multi-graviton theories where the usual strong coupling effects …
