Till Bargheer, Frank Coronado, Pedro Vieira
The octagon function is the fundamental building block yielding correlation functions of four large BPS operators in N=4 super Yang-Mills theory at any value of the 't Hooft coupling and at any genus order. Here we compute the octagon at strong coupling, and discuss various interesting limits and implications, both at the planar and non-planar level.
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We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system of nonlinear integro-differential equations which are powerful enough to fully determine their dependence on the 't Hooft coupling and two cross ratios. At weak coupling, solution to these equations yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we develop a systematic expansion of the octagon in the in…
We compute to all loop orders correlation function of four heavy BPS operators in $\mathcal{N}$= 4 SYM with special polarisations considered recently by Frank Coronado. Our main result is an expression for the octagon form factor as determinant of a semi-infinite matrix. We find that at weak coupling the entries of this matrix are linear combinations of ladder functions with simple rational coefficients and give the full perturbative expansion of the octagon.
We consider the so-called simplest correlation function of four infinitely heavy half-BPS operators in planar N=4 SYM in the limit when the operators are light-like separated in a sequential manner. We find a closed-form expression for the correlation function in this limit as a function of the 't Hooft coupling and residual cross ratios. Our analysis heavily relies on the factorization of the correlation function into the product of null octagons and on the recently established determinant representation for the latter. We show that the null octagon is given by a Fredholm determinant of a cer…
We explain how the 't Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in N=4 super Yang-Mills theory. The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number Nc of colors; the other variable is the octagon that contains all the 't Hooft coupling and spacetime dependence. At each genus g in the large Nc expansion, this function is a polynomial of degree 2g+2 in the octagon. We find several dual matrix model representations of the cor…
In the planar N = 4 supersymmetric Yang-Mills theory at weak coupling, we perform the first analytic computation of a two-loop eight-edged Wilson loop embedded into the boundary of AdS3. Its remainder function is given as a function of uniform transcendental weight four in terms of a constant plus a product of four logarithms. We compare to the strong-coupling result, and test a conjecture on the universality of the remainder function proposed in the literature.
We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar N=4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length. We show that the octagon can be expressed as the Fredholm determinant of the integrable Bessel operator and demonstrate that this representation is very efficient in finding the octagons both at weak and strong coupling. At weak coupling, in the limit when the four half-BPS operators become null separated in a sequential manner, the octagon obeys the Toda la…
A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by the square of the Fredholm determinant of a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives in terms of a two-dimensional Riemann-Hilbert problem. We solve the latter in the null limit making use of the Deift-Zhou steepest descent. We reproduce the exact octagonal anomalous dimension in 't Hooft coupling and provide its novel formulation as a convolution of the non-linear quasiclassical phase with the Fermi distribution in the limit of the infinit…
The simplest event shape in $\mathcal{N}=4$ super Yang--Mills
本研究针对平面$\boldsymbol{\text{N}=4}$超杨-米尔斯理论的两点事件形状，利用半BPS标量及其光变换构造源、汇与探测器，将其在大电荷极限下分解为两个八边形的乘积，进而分析其随耦合常数和探测器夹角的变化行为。
We study the maximally-helicity-violating (MHV) six-gluon scattering amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of "anomalous dimensions" that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon OPE, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string …
Positivity properties of observables in planar maximally supersymmetric Yang-Mills theory
研究平面N=4超杨-米尔斯理论中精确可观测量关于't Hooft耦合常数的Stieltjes正性性质，通过积分表示证明八边形反常维度等量的该性质，并用于获得非微扰界限和自举微扰系数。
Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
通过重组大't Hooft 耦合下行列式的 transseries，揭示了每个指数抑制修正与微扰级数的简单关系，为 cusp 反常维数、多胶子散射振幅和八边形形状因子等可观测量提供了高效生成完整 transseries 的方法，并用高精度数值分析验证了结果。
Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The coefficients of this expansion are decomposed in terms of several elementary building blocks and can be determined at finite 't Hooft coupling using bootstrap and integrability techniques. Some of these blocks are known from an analogous expansion of scattering amplitudes. In addition to these, the expansion for form factors includes a new type of building block…
In this paper, we studied the static dielectric function and interaction potential in strong coupling limit with AdS/CFT correspondence. The dielectric function is depressed compared with that in weak coupling. The interaction potential then presents a weaker screening characteristics in strong coupling, which indicates a smaller Debye mass compared with weak coupling.
The circular Wilson loop in the two-node quiver CFT is computed at large-N and strong 't Hooft coupling by solving the localization matrix model.
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak one, giving information from the nonperturbative region of the parameters space. It can be used to solve exactly power-type potentials and to extract deep information about the energy spectra of polynomial ones.
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In this note, we propose that the infrared structure of gluon amplitudes at strong coupling can be fully extracted from a local consideration near cusps. This is consistent with field theory and correctly reproduces the infrared divergences of the four-gluon amplitude at strong coupling calculated recently by Alday and Maldacena.
Two-dimensional large-$N$ quantum chromodynamics with scalar quarks is considered with particular emphasis on its strong coupling regime which has not been studied so far. Techniques necessary to deal with the infinitely oscillatory bound state wave functions in the strong coupling regime are developed. I derive an estimate for the ground state mass and show that (1) the lightest hadron in the theory is massless and (2) the ground state mass is continuous across the transition between the weak and the strong coupling.
A possibility of strong coupling quantum Liouville gravity is investigated via infinite dimensional representations of $\qslc$ with $q$ at a root of unity. It is explicitly shown that vertex operator in this model can be written by a tensor product of a vertex operator of the classical Liouville theory and that of weak coupling quantum Liouville theory. Some discussions about the strong coupling Liouville gravity within this formulation are given.
By studying the partition function of $N=4$ topologically twisted supersymmetric Yang-Mills on four-manifolds, we make an exact strong coupling test of the Montonen-Olive strong-weak duality conjecture. Unexpected and exciting links are found with two-dimensional rational conformal field theory.
We set up a systematic expansion of the prepotential for ${\cal N}=2$ supersymmetric Yang-Mills theories with SU(N) gauge group in the region of strong coupling where a maximal number of mutually local fields become massless. In particular, we derive the first non-trivial non-perturbative correction, which is the first term in the strong coupling expansion providing a coupling between the different U(1) factors, and which governs for example the strength of gaugino Yukawa couplings.
A strong-weak coupling duality symmetry of the string equations of motion has been suggested in the literature. This symmetry implies that vacua occur in pairs. Since the coupling constant is a dynamical variable in string theory, tunneling solutions between strong and weak coupling vacua may exist. Such solutions would naturally lead to nonperturbative effects with anomalous coupling dependence. A highly simplified example is given.
We give an exact analytic solution of the strong coupling limit of the integral equation which was recently proposed to describe the universal scaling function of high spin operators in N = 4 gauge theory. The solution agrees with the prediction from string theory, confirms the earlier numerical analysis and provides a basis for developing a systematic perturbation theory around strong coupling.
We introduce a method to compute from first principles the anomalous dimension of short operators in N=4 super Yang-Mills theory at strong coupling, where they are described in terms of superstring vertex operators in an anti-de Sitter background. We focus on the Konishi multiplet, dual to the first massive level of the superstring, and compute the one-loop correction to its anomalous dimension at strong coupling, using the pure spinor formalism for the superstring.
We perform the numerical simulation of the two dimensional chiral Gross Neveu model using the Kogut-Susskind(KS) fermion. In the case of SU(4), the Kosterlitz-Thouless phase transition happens at some critical value of the coupling constant. In the case of one flavour, there exists the strong coupling phase in which the correlation functions vanish and the general covariance is realized in the quantum field thoery through the dynamical process.
In this letter, we derive analytically the scaling dimension of the Konishi operator in planar N=4 gauge theory at strong coupling from the asymptotic Bethe equations. The first two leading terms agree with the recent string computation and numerical analysis of TBA equations. At the third order we find spurious logarithm of the coupling constant, which should be absent in the anomalous dimension of any finite operator of planar N=4 SYM theory. Showing the cancelation of this term would provide an important test at strong coupling for the recently proposed sets of TBA equations for planar AdS/…
We study the anisotropic Kardar-Parisi-Zhang equation using nonperturbative renormalization group methods. In contrast to a previous analysis in the weak-coupling regime we find the strong coupling fixed point corresponding to the isotropic rough phase to be always locally stable and unaffected by the anisotropy even at non-integer dimensions. Apart from the well-known weak coupling and the now well established isotropic strong coupling behavior, we find an anisotropic strong coupling fixed point for nonlinear couplings of opposite signs at non-integer dimensions.
With the dielectric function computed from AdS/CFT correspondence, we studied the wake potential induced by a fast moving charge in strong coupling plasma, and compared it with the weak coupling wake potential for different particle velocities as $v=0.55c$ and $v=0.99c$. The most prominent difference between strong and weak wake potential is that when $v=0.99c$ the remarkable oscillation due to Cerenkov-like radiation and Mach cone in weak coupling disappears in strong coupling, which implies that the plasmon mode with phase velocity lower than the speed of light dose not exist in strong coupl…
Motivations for the center vortex theory of confinement are discussed. In particular, it is noted that the abelian dual Meissner effect, which is the signature of dual superconductivity, cannot adequately describe the confining force at large distance scales. A long-range effective action is derived from strong-coupling lattice gauge theory in D=3 dimensions, and it is shown that center vortices emerge as the stable saddlepoints of this action. Thus, in the case of strong couplings, the vortex picture is arrived at analytically. I also respond briefly to a recent criticism regarding maximal ce…
We examine the potential strong coupling problem at early times in a bouncing cosmological model with "strong gravity in the past" (Jordan frame), which is conformally related to inflation (Einstein frame). From naive dimensional analysis in the Jordan frame one would conclude that the quantum strong coupling energy scale can be lower than the classical energy scale. However, from the Einstein frame prospective this should not be the case. We illustrate this point by calculation in the Jordan frame which shows cancellations of the dangerous contributions in the tree level amplitude.
This has been withdrawn by the author. A rewrite of some of the material is currently in progress.
In this letter we present our results for the four-loop beta-function of the strong coupling in the Standard Model of fundamental interactions. We take top-Yukawa and self-Higgs interactions into account, but neglect electroweak gauge couplings.
We show that introducing $R^2$-term makes the Higgs-inflation and Higgs-dilaton inflation consistent models: the strong coupling energy scales in scalar, gauge and gravity sectors all are lifted up to the Planck scale.
The relic abundance of stable neutralinos is investigated in $E_8 \times E_8'$ heterotic string theory when supersymmetry is spontaneously broken by hidden-sector gaugino condensates. In the weak coupling regime, very large scalar masses (compared to gaugino masses) are shown to lead to a too large relic abundance of the neutralinos, incompatible with cosmological observations in most of parameter space. The problem does not arise in the strong coupling regime (heterotic M-theory) because there scalar and gaugino masses are generically of the same order of magnitude.
We study time dependent solutions in dilaton gravity which correspond to the decay of conical spacetimes. In string theory this can be interpreted as a strong coupling limit of the decay of a non-supersymmetric orbifold spacetime with localized tachyons.
In the context of gravity in the strong-coupling regime, the propagation amplitude of gravity coupled to relativistic particles undergoing geodesic separation is calculated exactly. Geodesic separation gives rise to boundary terms associated with the h_\times and h_+ graviton components. At low temperatures the propagation amplitude vanishes, implying no graviton propagation in this regime.
I discuss various situations in which perturbative expansions are used in Yang-Mills theories with asymptotic freedom and establish the limits of its applicability.
Galilean Genesis is generically plagued with a strong coupling problem, but this can be avoided depending on the hierarchy between a classical energy scale of genesis and a strong coupling scale. In this paper, we investigate whether or not the models of Galilean Genesis without the strong coupling problem can explain the statistical properties of the observed CMB fluctuations based on two unified frameworks of Galilean Genesis. By focusing on the class in which the propagation speeds of the scalar and tensor perturbations are constant, we show that the models avoiding strong coupling and allo…
The Gell-Mann - Low function β(g) in QCD (g=g0^2/16π^2 where g0 is the coupling constant in the Lagrangian) is shown to behave in the strong-coupling region as β_\infty g^αwith α\approx -13, β_\infty\sim 10^5.
We analyze the resurgence properties of finite-dimensional exponential integrals which are prototypes for partition functions in quantum field theories. In these simple examples, we demonstrate that perturbation theory, even at arbitrarily weak coupling, fails as the argument of the coupling constant is varied. It is well-known that perturbation theory also fails at stronger coupling. We show that these two failures are actually intimately related. The formalism of resurgent transseries, which takes into account global analytic continuation properties, fixes both problems, and provides an arbi…
Transition from weak to strong coupling in thermal gauge theories: Lessons from ${\cal N}=4$ SYM Theory
本文利用Padé逼近插值热N=4 SYM理论中弱耦合与强耦合展开，确定两者之间转变的位置和宽度。
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