Hooft Coupling Limit Research Articles

Exploring the Quantum Spectral Curve for AdS3/CFT2

Despite the rich and fruitful history of the integrability approach to string theory on the AdS3 × S3 × T4 background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. In other integrable superstring backgrounds there is compelling evidence that this formulation captures all wrapping effects exactly and describes the full planar spectrum. This great success motivates us to study the new proposed QSC and develop methods to extract from it concrete predictions for spectral data. The AdS3 × S3 × T4 case presents a significant novel feature and challenge compared to its higher-dimensional analogues — massless modes. It has been conjectured that these manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for unprotected string excitations in the planar limit with finite quantum numbers and RR flux. We explain how to extract a systematic expansion around the analogue of the weak ’t Hooft coupling limit in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and also obtain high-precision numerical results. These concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.

Harnessing S-duality in mathcal{N} = 4 SYM & supergravity as SL(2, ℤ)-averaged strings

We develop a new approach to extracting the physical consequences of S-duality of four-dimensional mathcal{N} = 4 super Yang-Mills (SYM) and its string theory dual, based on SL(2, ℤ) spectral theory.We observe that CFT observables \U0001d4aa, invariant under SL(2, ℤ) transformations of a complexified gauge coupling τ, admit a unique spectral decomposition into a basis of square-integrable functions. This formulation has direct implications for the analytic structure of mathcal{N} = 4 SYM data, both perturbatively and non-perturbatively in all parameters. These are especially constraining for the structure of instantons: k-instanton sectors are uniquely determined by the zero- and one-instanton sectors, and Borel summable series around k-instantons have convergence radii with simple k-dependence. In large N limits, we derive the existence and scaling of non-perturbative effects, in both N and the ‘t Hooft coupling, which we exhibit for certain mathcal{N} = 4 SYM observables. An elegant benchmark for these techniques is the integrated stress tensor multiplet four-point function, conjecturally determined by [1] for all τ for SU(N) gauge group; we elucidate its form, and explain how the SU(2) case is the simplest possible observable consistent with SL(2, ℤ)-invariant perturbation theory.These results have ramifications for holography. We explain how leftlangle mathcal{O}rightrangle , the ensemble average of \U0001d4aa over the mathcal{N} = 4 supersymmetric conformal manifold with respect to the Zamolodchikov measure, is cleanly isolated by the spectral decomposition. We prove that the large N limit of leftlangle mathcal{O}rightrangle equals the large N, large ‘t Hooft coupling limit of \U0001d4aa. Holographically speaking, leftlangle mathcal{O}rightrangle = \U0001d4aasugra, its value in type IIB supergravity on AdS5× S5. This result, which extends to all orders in 1/N, embeds ensemble averaging into the traditional AdS/CFT paradigm. The statistics of the SL(2, ℤ) ensemble exhibit both perturbative and non-perturbative 1/N effects. We discuss further implications and generalizations to other AdS compactifications of string/M-theory.

Correction to baryon spectrum in holographic QCD

We study solitons in the context of Sakai-Sugimoto-Witten holographic model of QCD. In the large 't Hooft coupling limit, flat space instantons give an approximate description of baryons. We provide an ansatz through deforming the BPST instanton by zero modes and obtain a subleading correction to the effective action. We also consider the quantum mechanical description of the collective coordinates. The correction term appears as a perturbation to the potential of the Hamiltonian and hence we can derive a first order correction to the mass spectrum of baryons.

Decay properties of Roper resonance in the holographic QCD

We investigate the one pion decay of the Roper resonance $N^*(1440)$$\to$$N$${\pi}$ in the Sakai-Sugimoto model of the holographic QCD. The nucleon and Roper resonance emerge as ground and first excited states of the collective radial motion of the instanton in the four dimensional space with one extra dimension. It is found that the ratio of the ${\pi}$$NN^*$ and ${\pi}$$NN$ couplings, and hence the ratio of $g_A^{NN^*}$ and $g_A^{NN}$, is well reproduced in comparison with the experimental data. The mechanism of this result is due to the collective nature of excitations, which is very different from that of the single particle nature of the constituent quark model. Our results are obtained in the large-$N_c$ and large ${\lambda}$ ('t~Hooft coupling) limit which are useful to test how baryon resonances share what are expected in these limits.

Extremal correlators and random matrix theory

We study the correlation functions of Coulomb branch operators of four-dimensional mathcal{N} = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

The QCD trace anomaly at strong coupling from M-theory

Obtaining a lattice-consistent result for the temperature dependence of the QCD conformal anomaly from a top-down M-theory dual (valid) for all temperatures – both, T<T_c and T>T_c – of thermal QCD at intermediate gauge coupling, has been missing in the literature. We fill this gap by addressing this issue from the M-theory uplift of the SYZ type IIA mirror at intermediate gauge/string coupling [both obtained in Dhuria et al. (JHEP 1311:001, 2013)] of the UV-complete type IIB holographic dual of large-N thermal QCD of Mia et al. (Nucl Phys B 839:187, 2010), and comparing with the very recent lattice results of Bazavov et al. (Phys Rev D 97(1):014510, 2018). Estimates of the mathcal{O}(R^4) higher derivative corrections in the D=11 supergravity action relevant to considering the aforementioned M theory uplift in the intermediate ’t Hooft coupling (in addition to gauge coupling) limit, are also presented. We also show that after a tuning of the (small) Ouyang embedding parameter and radius of a blown-up S^2 when expressed in terms of the horizon radius, a QCD deconfinement temperature T_c=150 MeV from a Hawking–Page phase transition at vanishing baryon chemical potential consistent with lattice QCD in the heavy-quark limit, can be obtained.

Mathcal{N} = 2 conformal gauge theories at large R-charge: the SU(N) case

Conformal theories with a global symmetry may be studied in the double scaling regime where the interaction strength is reduced while the global charge increases. Here, we study generic 4d mathcal{N} = 2 SU(N ) gauge theories with conformal matter content at large R-charge QR → ∞ with fixed ’t Hooft-like coupling kappa ={Q}_{mathrm{R}}{g}_{mathrm{YM}}^2. Our analysis concerns two distinct classes of natural scaling functions. The first is built in terms of chiral/anti-chiral two-point functions. The second involves one-point functions of chiral operators in presence of frac{1}{2} -BPS Wilson-Maldacena loops. In the rank-1 SU (2) case, the two-point sector has been recently shown to be captured by an auxiliary chiral random matrix model. We extend the analysis to SU(N) theories and provide an algorithm that computes arbitrarily long perturbative expansions for all considered models, parametric in the rank. The leading and next-to-leading contributions are cross-checked by a three- loops computation in mathcal{N} = 1 superspace. This perturbative analysis identifies maximally non-planar Feynman diagrams as the relevant ones in the double scaling limit. In the Wilson-Maldacena sector, we obtain closed expressions for the scaling functions, valid for any rank and κ. As an application, we analyze quantitatively the large ’t Hooft coupling limit κ ≫ 1 where we identify all perturbative and non-perturbative contributions. The latter are associated with heavy electric BPS states and the precise correspondence with their mass spectrum is clarified.

AdS4/CFT3 from weak to strong string coupling

We consider the four-point function of operators in the stress tensor multiplet of the U(N)k× U(N)−k ABJM theory, in the limit where N is taken to infinity while N/k5 is held fixed. In this limit, ABJM theory is holographically dual to type IIA string theory on AdS4× ℂℙ3 at finite string coupling gs∼ (N/k5)1/4. While at leading order in 1/N, the stress tensor multiplet four-point function can be computed from type IIA supergravity, in this work we focus on the first subleading correction, which comes from tree level Witten diagrams with an R4 interaction vertex. Using superconformal Ward identities, bulk locality, and the mass deformed sphere free energy previously computed to all orders in 1/N from supersymmetric localization, we determine this R4 correction as a function of N/k5. Taking its flat space limit, we recover the known R4 contribution to the type IIA S-matrix and reproduce the fact that it only receives perturbative contributions in gs from genus zero and genus one string worldsheets. This is the first check of AdS/CFT at finite gs for local operators. Our result for the four-point correlator interpolates between the large N, large ’t Hooft coupling limit and the large N finite k limit. From the bulk perspective, this is an interpolation between type IIA string theory on AdS4× ℂℙ3 at small string coupling and M-theory on AdS4× S7/ℤk.

Four-point functions of all-different-weight chiral primary operators in the supergravity approximation

Recently a Mellin-space formula was conjectured for the form of correlation functions of 1/2 BPS operators in planar mathcal{N}=4 SYM in the strong ’t Hooft coupling limit. In this work we report on the computation of two previously unknown four-point functions of operators with weights 〈2345〉 and 〈3456〉, from the effective type-IIB supergravity action using AdS/CFT. These correlators are novel: they are the first correlators with all different weights and in particular 〈3456〉 is the first next-next-next-to-extremal correlator to ever have been computed. We also present simplifications of the known algorithm, without which these computations could not have been executed. These simplifications consist of a direct formula for the exchange part and for the contact part of the correlation function, as well as a simplification of the C tensor algorithm to compute a tensors. After bringing our results in the appropriate form we successfully corroborate the recently conjectured formula.

Gravity dual of two-dimensional mathcal{N} = (2, 2)\u2217 supersymmetric Yang-Mills theory and integrable models

The 2D mathcal{N} = (2, 2)∗ supersymmetric Yang-Mills theory can be obtained from the 2D mathcal{N} = (4, 4) theory with a twisted mass deformation. In this paper we construct the gravity dual theory of the 2D mathcal{N} = (2, 2)∗ supersymmetric U(N ) Yang-Mills theory at the large N and large ’t Hooft coupling limit using the 5D gauged supergravity. In the UV regime, this construction also provides the gravity dual of the 2D mathcal{N} = (2, 2)∗ U(N ) topological Yang-Mills-Higgs theory. We propose a triality in the UV regime among integrable model, gauge theory and gravity, and we make some checks of this relation at classical level.

From the Sakai-Sugimoto model to the generalized Skyrme model

We derive the generalized Skyrme model as a low-energy effective model of the Sakai-Sugimoto model. The novelty with the past is the presence of the sextic term equal to the topological charge squared. This term appears when the $\omega$ meson, and the tower of states on top of it, are integrated out. We claim that, in the small 't Hooft coupling limit, the instanton is well described by a Skyrmion arising from the low energy effective Lagrangian of the Sakai-Sugimoto model. The sextic term plays a dominant role in this limit. Moreover, when a pion mass term is added we recover the BPS Skyrme model in the small 't Hooft coupling limit.

Strong coupling limit of a family of Chern-Simons-matter theories

We investigate the strong coupling limit of a family of Chern-Simons-matter theories in the planar limit. The family consists of mathcal{N}=3 theories with the gauge group mathrm{U}{left({N}_1right)}_{k_1} times mathrm{U}{left({N}_2right)}_{k_{{}_2}} coupled to n bi-fundamental hypermultiplets. All observables which can be determined from the planar resolvent turn out to have finite limits in the large ’t Hooft coupling limit. Possible gravity duals are briefly discussed. We observe that Kac-Moody algebras govern the structure of the planar spectral curves of the theories.

Top\u2013down holographic G-structure glueball spectroscopy at (N)LO in N and finite coupling

The top–down type IIB holographic dual of large-N thermal QCD as constructed in Mia et al. (Nucl Phys B 839:187, 2010) involving a fluxed resolved warped deformed conifold, its delocalized type IIA Strominger–Yau–Zaslow-mirror (SYZ-mirror) as well as its M-theory uplift constructed in Dhuria and Misra (JHEP 1311:001, 2013) – both in the finite coupling (g_smathop {sim }limits ^{<}1)/‘MQGP’ limit of Dhuria and Misra (JHEP 1311:001, 2013) – were shown explicitly to possess a local SU(3)/G_2-structure in Sil and Misra (Nucl Phys B 910:754, 2016). Glueballs spectra in the finite-gauge-coupling limit (and not just large ’t Hooft coupling limit) – a limit expected to be directly relevant to strongly coupled systems at finite temperature such as QGP (Natsuume in String theory and quark–gluon plasma, 2007) – has thus far been missing in the literature. In this paper, we fill this gap by calculating the masses of the 0^{++}, 0^{-+},0^{{-}{-}}, 1^{++}, 2^{++} (‘glueball’) states (which correspond to fluctuations in the dilaton or complexified two-forms or appropriate metric components) in the aforementioned backgrounds of G-structure in the ‘MQGP’ limit of Dhuria and Misra (JHEP 1311:001, 2013). We use WKB quantization conditions on one hand and impose Neumann/Dirichlet boundary conditions at an IR cut-off (‘r_0’)/horizon radius (‘r_h’) on the solutions to the equations of motion on the other hand. We find that the former technique produces results closer to the lattice results. We also discuss the r_h=0 limits of all calculations. In this context we also calculate the 0^{++}, 0^{{-}{-}},1^{++}, 2^{++} glueball masses up to Next to Leading Order (NLO) in N and find a frac{g_sM^2}{N}(g_sN_f)-suppression similar to and further validating semi-universality of NLO corrections to transport coefficients, observed in Sil and Misra (Eur Phys J C 76(11):618, 2016).

One-loop free energy of tensionless type IIB string in AdS5\xd7S5

Considering the zero ’t Hooft coupling limit of mathcal{N}=4 super-Yang-Mills theory, the exact spectrum of all single-trace operators can be accessed in terms of the underlying so(2, 4) character. This makes it possible in turn to compute the one-loop free energy of the tensionless type IIB string theory in AdS5×S5 background, with help of the recently developed method of character integral representation of zeta function (CIRZ). We calcu-late first the one-loop free energy of the string states in the (p − 1)-th Regge trajectory and find the result to be p times the free energy of a single mathcal{N}=4 Maxwell multiplet. The full one-loop free energy is hence proportional to the divergent series {displaystyle {sum}_{p=2}^{{}_{infty }}p} . The divergence arises as a result of interrupting the regularization procedure in an intermediate stage. With a reorganization of states, we extract the finite part of free energy after summing over the Regge trajectories. This way gives us a finite result which is minus of the free energy of the mathcal{N}=4 multiplet. Hence, this bulk one-loop result matches the −1 term in the N2− 1 factor of the boundary result.

Nonlinear Schrödinger Equation, 2D N = (2, 2)* Topological Yang-Mills-Higgs Theory and Their Gravity Dual

The duality between the N-particle sector of quantum nonlinear Schrödinger equation and the 2D N = (2, 2)* U(N) topological Yang-Mills-Higgs theory was found by Gerasimov and Shatashvili some time ago. At the large N and large ’t Hooft coupling limit, the gravity dual of the 2D N = (2, 2)* U(N) topological Yang-Mills-Higgs theory can be constructed. Consequently, as a first example, one can formulate a triangle relation between integrable model, gauge theory and gravity. We present the results of the gravity dual in this paper, and make some checks at classical level between the gravity dual and the nonlinear Schrödinger equation. This paper is based on the talk given by the author at the 24th International Conference on Integrable Systems and Quantum Symmetries, and more details can be found in Ref. [].

Exploring nonlocal observables in shock wave collisions

We study the time evolution of 2-point functions and entanglement entropy in strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills theory in the large N and large 't Hooft coupling limit using AdS/CFT. On the gravity side this amounts to calculating the length of geodesics and area of extremal surfaces in the dynamical background of two colliding gravitational shockwaves, which we do numerically. We discriminate between three classes of initial conditions corresponding to wide, intermediate and narrow shocks, and show that they exhibit different phenomenology with respect to the nonlocal observables that we determine. Our results permit to use (holographic) entanglement entropy as an order parameter to distinguish between the two phases of the cross-over from the transparency to the full-stopping scenario in dynamical Yang-Mills plasma formation, which is frequently used as a toy model for heavy ion collisions. The time evolution of entanglement entropy allows to discern four regimes: highly efficient initial growth of entanglement, linear growth, (post) collisional drama and late time (polynomial) fall off. Surprisingly, we found that 2-point functions can be sensitive to the geometry inside the black hole apparent horizon, while we did not find such cases for the entanglement entropy.

Thermal quench at finite 't Hooft coupling

Using holography we have studied thermal electric field quench for infinite and finite 't Hooft coupling constant. The set-up we consider here is D7-brane embedded in (α′ corrected) AdS-black hole background. It is well-known that due to a time-dependent electric field on the probe brane, a time-dependent current will be produced and it will finally relax to its equilibrium value. We have studied the effect of different parameters of the system on equilibration time. As the most important results, for massless fundamental matter, we have observed a universal behaviour in the rescaled equilibration time in the very fast quench regime for different values of the temperature and α′ correction parameter. It seems that in the slow quench regime the system behaves adiabatically. We have also observed that the equilibration time decreases in finite 't Hooft coupling limit.

Precision calculation of 1/4-BPS Wilson loops in AdS5×S5

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$_5\times$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 Gel'fand-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.

Logarithmic corrections to the entanglement entropy

In a $d$-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $\Delta=\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, we can investigate such a logarithmic correction holographically by deforming an AdS space with a massive scalar field dual to the operator with $\Delta=\frac{d+2}{2}$. There are two sources generating the logarithmic correction. One is the metric deformation and the other is the minimal surface deformation. In this work, we investigate the change of the entanglement entropy caused by the minimal surface deformation and find that the second order minimal surface deformation leads to an additional logarithmic correction.

Vacuum instability in electric fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian thermalization

We analyze vacuum instability of strongly coupled gauge theories in a constant electric field using AdS/CFT correspondence. The model is the $ \mathcal{N}=2 $ 1-flavor supersymmetric large N c QCD in the strong ’t Hooft coupling limit. We calculate the Euler-Heisenberg effective Lagrangian $ \mathcal{L} $ (E), which encodes the nonlinear response and the quantum decay rate of the vacuum in a background electric field E, from the complex D-brane action in AdS/CFT. We find that the decay rate given by Im $ \mathcal{L} $ (E) becomes nonzero above a critical electric field set by the confining force between quarks. A large E expansion of Im $ \mathcal{L} $ (E) is found to coincide with that of the Schwinger effects in QED, replacing its electron mass by the confining force. Then, the time-dependent response of the system in a strong electric field is solved non-perturbatively, and we observe a universal thermalization at a shortest timescale “Planckian thermalization time” $ {\tau_{\mathrm{th}}}\sim \frac{\hbar }{{{k_B}T_{\mathrm{eff}}^{\infty }}}\sim \frac{\hbar }{{{k_B}}}{E^{{-{1 \left/ {2} \right.}}}} $ . Here, $ T_{\mathrm{eff}}^{\infty } $ is an effective temperature which quarks feel in the nonequilibrium state with nonzero electric current, calculated in AdS/CFT as a Hawking temperature. Stronger electric fields accelerate the thermalization, and for a realistic value of the electric field in RHIC experiment, we obtain τ th ~ 1 [fm/c], which is consistent with the believed value.