Supersymmetric Yang-Mills Theory Research Articles

A first look at the function space for planar two-loop six-particle Feynman integrals

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle processes. In this paper, we initiate the study of the function space for planar two-loop six-particle processes. We study all genuine six-particle Feynman integrals, and derive the differential equations they satisfy on maximal cuts. Performing a leading singularity analysis in momentum space, and in Baikov representation, we find an integral basis that puts the differential equations into canonical form. The corresponding differential equation in the eight independent kinematic variables is derived with the finite-field reconstruction method and the symbol letters are identified. We identify the dual conformally invariant hexagon alphabet known from maximally supersymmetric Yang-Mills theory as a subset of our alphabet. This paper constitutes an important step in the analytic calculation of planar two-loop six-particle Feynman integrals.

Precision holography for 5D Super Yang-Mills

We study 1/2-BPS Wilson loop (WL) operators in maximally supersymmetric Yang-Mills theory (MSYM) on S5. Their vacuum expectation value (vev) can be computed exactly at large N thanks to supersymmetric localization. The holographic dual to MSYM on S5 is geometrically realized by a stack of N D4-branes with spherical worldvolume in ten dimensions. We compute the vev of the circular WL using holography by evaluating the partition function of a fundamental string in this background. Our focus is on the next-to-leading order correction to the string partition function which is composed of two parts; the dilaton coupling to the worldsheet and the one-loop fluctuations of the worldsheet itself. We face a variety of issues, some related to the presence of a non-constant dilaton, and others that are common to its AdS analogue. However, the universality of UV divergences as well as the importance of a proper choice of an IR regulator have been recently stressed in the literature. Inspired by this, we resolve our issues by first carefully treating the Weyl anomaly which receives contributions from the non-constant dilaton, and then by computing the ratio of our partition function and the one of a string in AdS4×CP3, which is dual to a 1/2-BPS WL in ABJM. Crucially, this approach yields a finite result which matches the corresponding ratio of WL vevs on the gauge theory side.

N=4 supersymmetric Yang-Mills thermodynamics from effective field theory

The free energy density of $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions is derived through second order in the 't Hooft coupling $\ensuremath{\lambda}$ at finite temperature using effective-field theory methods. The contributions to the free energy density at this order come from the hard scale $T$ and the soft scale $\sqrt{\ensuremath{\lambda}}T$. The effects of the scale $T$ are encoded in the coefficients of an effective three-dimensional field theory that is obtained by dimensional reduction at finite temperature. The effects of the electric scale $\sqrt{\ensuremath{\lambda}}T$ are taken into account by perturbative calculations in the effective theory.

Two-loop amplitudes for di-Higgs and di-pseudo-Higgs productions through quark annihilation in QCD

Through this article, we present the two-loop massless QCD corrections to the production of di-Higgs and di-pseudo-Higgs boson through quark annihilation in the large top quark mass limit. Within dimensional regularisation, we employ the non-anticommuting γ5 and treat it under the Larin prescription. We discover the absence of any additional renormalisation, so-called contact renormalisation, that could arise from the short distance behaviour of two local operators. This finding is in corroboration with the operator product expansion. By examining the results, we discover the lack of similarity in the highest transcendentality weight terms between these finite remainders and that of a pair of half-BPS primary operators in maximally supersymmetric Yang-Mills theory. We need these newly computed finite remainders to calculate observables involving di-Higgs or di-pseudo- Higgs at the next-to-next-to-leading order. We implement the results to a numerical code for further phenomenological studies.

Prescriptive unitarity with elliptic leading singularities

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that diagonalizing with respect to these leading singularities ensures that the integrand basis is term-wise pure (suitably generalized, to the elliptic multiple polylogarithms, as necessary). We also investigate an alternative strategy based on diagonalizing a basis of integrands on differential forms; this strategy, while neither term-wise Yangian-invariant nor pure, offers several advantages in terms of complexity.

The three-loop MHV octagon from overline{Q} equations

The overline{Q} equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar mathcal{N} = 4 supersymmetric Yang-Mills theory. By using the overline{Q} equations, we compute the symbol of the first MHV amplitude with algebraic letters — the three-loop 8-point amplitude (or the octagon remainder function) — in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) mathcal{N} = 4 SYM

The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) mathcal{N} = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/ {g}_{YM}^2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ( {g}_{YM}^2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O( {g}_{YM}^{-2w} ) when {g}_{YM}^2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form {overline{q}}^{left|kright|}hat{f}left({g}_{YM}right) , where hat{f}left({g}_{YM}right)=Oleft({g}_{YM}^{2w}right) when {g}_{YM}^2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

Finding AdS5\xd7 S5 in 2+1 dimensional SCFT physics

We study solutions of type IIB string theory dual to mathcal{N} = 4 supersymmetric Yang-Mills theory on half of ℝ3,1 coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically AdS5×S5 with boundary geometry ℝ2,1×ℝ+, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré AdS5×S5. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily far towards the missing asymptotic region, recovering the “missing” half of Poincaré AdS5×S5. We also show that there are 3D SCFTs whose dual includes a wedge of Poincaré AdS5×S5 with an angle arbitrarily close to π, with geometrical ETW branes on either side.

Finite-N superconformal index via the AdS/CFT correspondence

Abstract We propose a prescription to calculate the superconformal index of the ${\cal N}=4$U(N) supersymmetric Yang–Mills theory with finite N on the anti-de Sitter side. The finite-N corrections are included as contributions of D3-branes wrapped around three-cycles in ${\boldsymbol S}^5$, which are calculated as the index of the gauge theories realized on the wrapped branes. The single-wrapping contribution has been studied in a previous work, and we further confirm that the inclusion of multiple-wrapping contributions correctly reproduces the higher-order terms as far as we have checked numerically.

Three-Loop Color-Kinematics Duality: A 24-Dimensional Solution Space Induced by New Generalized Gauge Transformations.

We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and also of a length-3 half-Bogomol'nyi-Prasad-Sommerfield operator in N=4 supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity. The integrand results are verified by all planar and nonplanar unitarity cuts, and they satisfy the minimal power counting of loop momenta and diagrammatic symmetries. Interestingly, these three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors. We also perform numerical integration and obtain consistent full-color infrared divergences and the known planar remainder. The form factors we obtain can be understood as the N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter.

Treating divergent perturbation theory: Lessons from exactly solvable 2D models at large N

We consider the operator product expansion (OPE) of correlation functions in the supersymmetric $O(N)$ non-linear sigma model at sub-leading order in the large $N$ limit in order to study the cancellation between ambiguities coming from infrared renormalons and those coming from various operators in the OPE. As has been discussed in the context of supersymmetric Yang-Mills theory in four dimensions, supersymmetry presents a challenge to this cancellation. In a bid to solve this problem we consider $O(N)$ as a toy model. A background field method inspired by Polyakov's treatment of the renormalization of the bosonic $O(N)$ model is used to identify explicit operators in the OPE of the two-point functions of bosonic and fermionic fields in the model. In order to identify the coefficient functions in the OPE, the exact two-point functions at sub-leading order in large $N$ are expanded in powers of the natural infrared length scale. The ambiguities arising from renormalons in the coefficient functions and vacuum expectation values of operators in the OPE are shown to cancel to all orders. The question of supersymmetric Yang-Mills theory without matter remains open.

Bootstrapping the half-BPS line defect CFT in N=4 supersymmetric Yang-Mills theory at strong coupling

The authors apply bootstrap methods to the half-BPS Wilson line with local operator insertions (defects) in the four-dimensional maximally supersymmetric (N = 4) Yang-Mills theory. They extract analitically the scaling dimension of the lightest non-protected scalar operator to the fourth order in the strong coupling expansion (t'Hooft coupling).

Novel 3D supersymmetric massive Yang-Mills theory

We construct three-dimensional, $\mathcal{N}=1$ off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is ``third-way'' consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

On the superconformal index of Chern-Simons theories and their KK spectrometry

We study the large-N limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with mathcal{N} = 2 supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we need a refinement of the gravity index which reflects the fact that the UV description on the field theory side has enhanced global symmetry.

Novel wall-crossing behaviour in rank one mathcal{N} = 2* gauge theory

We study the BPS spectrum of four-dimensional mathcal{N} = 2 supersymmetric Yang-Mills theory with gauge group SU(2) and a massive adjoint hypermultiplet, which has an extremely intricate structure with infinite spectrum in all chambers of its Coulomb moduli space, and is not well understood. We build on previous results by employing the BPS quiver description of the spectrum, and explore the qualitative features in detail using numerical techniques. We find novel and unexpected behaviour in the form of wall-crossings involving interactions between BPS particles with negative electric-magnetic pairings, which we interpret in terms of the reverse orderings of the usual wall-crossing formulas for rank one mathcal{N} = 2 field theories. This identifies new a priori unrelated states in the spectrum.

Quantum simulation of gauge theory via orbifold lattice

We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge theories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.

4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

Stabilization of the extended horizons

We extend Kodama-Ishibashi and Jansen-Rostworowski-Rutkowski master field framework to study quasinormal modes of black branes and black holes of Einstein gravity in $D=5$ space-time dimensions with multiple scalars and an arbitrary bulk potential. As an application, we consider a thermodynamically unstable state of mass deformed ${\cal N}=4$ supersymmetric Yang-Mills theory at strong coupling. The corresponding gravitational dual is ${\cal N}=2^*$ black brane with a dynamical instability of its translationary invariant horizon. We study the dependence of the quasinormal mode spectra as the boundary gauge theory is compactified on $S^3$ -- the black brane is turned into the black hole.

The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL\u2032

We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N3LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N3LO. We combine the newly obtained N3LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in mathcal{N} = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N3LL′ accuracy, resulting in a factor of ∼ 4 reduction of uncertainties in the peak region compared to N3LL predictions.

Four-loop collinear anomalous dimensions in QCD and [formula omitted] super Yang-Mills

We calculate the collinear anomalous dimensions in massless four-loop QCD and N=4 supersymmetric Yang-Mills theory from the infrared poles of vertex form factors. We give very precise numerical approximations and a conjecture for the complete analytic results in both models we consider.