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At least 469 records · Page 26
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DOE OSTI2025

Rational QCD loop amplitudes and quantum theories on twistor space

We show how curing an anomaly of the twistor uplift of self-dual Yang-Mills theory implies linear relations among one-loop, n-gluon, color-ordered subamplitudes in QCD, when all n gluon helicities are positive, or when exactly one is negative. We compute the number of linearly independent subamplitudes as determined by these relations, in terms of unsigned Stirling numbers. Then we use a momentum-twistor parametrization to show that there are no further linear dependencies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Symbol alphabets from plabic graphs II: rational letters

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n = 8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of G + (n-4, n).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A three-point form factor through five loops

We bootstrap the three-point form factor of the chiral part of the stress­tensor supermultiplet in planar $\mathcal{N}$ = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ * → $q\overline{q}g$. We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $\mathcal{N}$ = 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of N = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in N = 4 DBI) are shown to be removable at O(ε 0 ) by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

2-Group global symmetries and anomalies in six-dimensional quantum field theories

We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength ƒ (2) , naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ~ * Tr (ƒ (2) $\wedge$ ƒ (2) ). We show that suitable mixed anomalies involving the gauge field ƒ (2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J (2) . We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a -type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Logarithmic corrections to the entropy of rotating black holes and black strings in AdS 5

We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS 5 black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined, on the field theory side, by the superconformal index and the refined topologically twisted index of $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory, respectively. We read off the logarithmic correction from those field-theoretic partition functions. On the gravity side, we take the near-horizon limit and apply the Kerr/CFT correspondence whose associated charged Cardy formula describes the degeneracy of states at subleading order and determines the logarithmic correction to the entropy. We find perfect agreement between these two approaches. Our results provide a window into precision microstate counting and demonstrate the efficacy of low-energy, symmetry-based approaches such as the Kerr/CFT correspondence for asymptotically AdS black objects under certain conditions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Finite N indices and the giant graviton expansion

The superconformal index of N = 4 super-Yang Mills theory with U(N) gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for the case of a single giant graviton. Here we give similar explicit formulae for an arbitrary number, m ≥ 1, of giant gravitons. We provide 1/2 and 1/16 BPS index examples up to the order where three giant gravitons contribute and demonstrate that the expansion of the matrix integral differs from the giant graviton expansion computed in the supergravity dual. This shows that the giant graviton expansion is not necessarily unique once two or more giant gravitons start appearing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

One-loop corrections to the celestial chiral algebra from Koszul Duality

We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its lift to holomorphic BF theory on twistor space. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using Koszul duality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Soft and collinear limits in $\mathcal{N}$ = 8 supergravity using double copy formalism

It is known that $\mathcal{N}$ = 8 supergravity is dual to $\mathcal{N}$ = 4 super Yang-Mills (SYM) via the double copy relation. Using the explicit relation between scattering amplitudes in the two theories, we calculate the soft and collinear limits in $\mathcal{N}$ = 8 supergravity from know results in $\mathcal{N}$ = 4 SYM. In our application of double copy, a particular self-duality condition is chosen for scalars that allows us to constrain and determine the R-symmetry indices of the supergravity states in the collinear limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Multi-matrix correlators and localization

Abstract We study generating functions of$$ \frac{1}{4} $$ 1 4 -BPS states in$$ \mathcal{N} $$ N = 4 super Yang-Mills at finiteNby attempting to generalize the Harish-Chandra-Itzykson-Zuber integral to multiple commuting matrices. This allows us to compute the overlaps of two or more generating functions; such calculations arise in the computation of two-point correlators in the free-field limit. We discuss the four-matrix HCIZ integral in the U(2) context and lay out a prescription for finding a more general formula forN> 2. We then discuss its connections with the restricted Schur polynomial operator basis. Our results generalize readily to arbitrary numbers of matrices, opening up the opportunity to study more generic BPS operators.

Physics↗
DOE OSTI2020

Sign flip triangulations of the amplituhedron

We present new triangulations of the m = 4 amplituhedron relevant for scattering amplitudes in planar N = 4 super-Yang-Mills, obtained directly from the combinatorial definition of the geometry. Using the “sign flip” characterization of the amplituhedron, we reproduce the canonical forms for the all-multiplicity next-tomaximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (N2MHV) tree-level as well as the NMHV one-loop cases, without using any input from traditional amplitudes methods. Our results provide strong evidence for the equivalence of the original definition of the amplituhedron [1] and the topological one [2], and suggest a new path forward for computing higher loop amplitudes geometrically. In particular, we realize the NMHV one-loop amplituhedron as the intersection of two amplituhedra of lower dimensionality, which is reflected in the novel structure of the corresponding canonical form.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Soft gluon emission at two loops in full color

The soft emission factor is a central ingredient in the factorization of generic n-particle gauge theory amplitudes with one soft gluon in the external state. We present the complete two-loop soft factor, capturing the leading power behavior in the soft-gluon momentum. At two loops, the color structure and the kinematic dependence of the soft factor become nontrivial as the soft gluon can couple to three hard partons for the first time (tripole terms). The nontrivial kinematic dependence of the tripole terms is of uniform, maximal transcendental weight, and can be expressed (in a “Euclidean” region) in terms of single-valued harmonic polylogarithms. Our results are consistent with the behavior of the recently computed symbol of the two-loop five-particle amplitude in $Ν$ = 4 super-Yang-Mills theory. In the limit where the outgoing soft gluon is also collinear with an incoming hard parton, potentially dangerous factorization-violating terms can arise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Celestial gluon amplitudes from the outside in

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D ‘gluon’ operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Revisiting single inclusive jet production: timelike factorization and reciprocity

Factorization theorems for single inclusive jet production play a crucial role in the study of jets and their substructure. In the case of small radius jets, the dynamics of the jet clustering can be factorized from both the hard production dynamics, and the dynamics of the low scale jet substructure measurement, and is described by a matching coefficient that can be computed in perturbative Quantum Chromodynamics (QCD). A proposed factorization formula describing this process has been previously presented in the literature, and is referred to as the semi-inclusive, or fragmenting jets formalism. By performing an explicit two-loop calculation, we show the inconsistency of this factorization formula, in agreement with another recent result in the literature. Building on recent progress in the factorization of single logarithmic observables, and the understanding of reciprocity, we then derive a new all-order factorization theorem for inclusive jet production. The use of a jet algorithm, being only a modification of the infrared structure of the measurement, modifies the structure of convolutions in the factorization theorem, as compared to inclusive fragmentation, but maintains the universality of the inclusive hard function and its associated Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution, which are ultraviolet properties. However, the non-trivial structure of convolutions in the factorization theorem implies that the jet functions exhibit a modified evolution. We perform an explicit two-loop calculation of the jet function in both N = 4 super Yang-Mills (SYM), and for all color channels in QCD, finding exact agreement with the structure derived from our renormalization group equations. In addition, we derive several new results, including an extension of our factorization formula to jet substructure observables, a jet algorithm definition of a generating function for the energy correlators, and new results for exclusive jet functions. Our results are a key ingredient for achieving precision jet substructure at colliders.

Effective Field Theories↗
DOE OSTI2025

Two-loop MHV form factors from the periodic Wilson loop

We discuss how to compute maximal-helicity-violating (MHV) form factors for the chiral part of the stress-tensor supermultiplet from periodic light-like polygon Wilson loops in planar $\mathcal{N}$ = 4 super Yang-Mills theory beyond the one-loop level. We show that the periodicity imposes path ordering on points on different edges, which explains the appearance of square roots coming from non-planar Feynman diagrams. Taking such diagrams into account, we provide the integrand of the two-loop n-particle MHV form factor, compute all diagrams, prove the cancellation of divergences and finally compute the two-loop 5-particle and 6-particle form factors as examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Effective gravitational couplings of four-dimensional $ \mathcal{N} $ = 2 supersymmetric gauge theories

The low energy effective couplings of a four-dimensional N = 2 supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions A and B. These two functions play an important role in the study of topologically twisted four-dimensional N = 2 supersymmetric gauge theories and in the computation of central charges of N = 2 superconformal theories. In this paper, we compute A and B from the partition function in the Ω-background for SU(2) gauge theories. Our results not only confirm the predicted expressions of the effective gravitational couplings, but also give the previously undetermined overall multiplicative factors. We also analyze A and B for the SU(N) super-Yang-Mills theory, and confirm all the previous predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Universality between vector-like and chiral quiver gauge theories: anomalies and domain walls

We study low-energy dynamics of [SU($\textit{N}$)]$^K$ chiral quiver gauge theories in connection with $\mathcal{N}$ = 1 super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by $\mathbb Z_K$ orbifold projections of $\mathcal{N}$ = 1 SU($\textit{N K}$) SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for $\textit{K}$ ≥ 3. In order to study low-energy behaviors, we analyze these systems using ’t Hooft anomaly matching and reliable semiclassics on $\mathbb R^3 × S^1$. Thanks to ’t Hooft anomaly that involves 1-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist $\textit{N}$ vacua. Theories with even $\textit{K}$ possess a physical θ angle despite the presence of massless fermions, and we further predict the $\textit{N}$-branch structure associated with it; the number of vacua is enhanced to 2$\textit{N}$ at θ = π due to spontaneous $\textit{C P}$ breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on $\mathbb R^3 × S^1$ with the double-trace deformation. Symmetry and anomaly of odd-$\textit{K}$ theories are the same as those of the $\mathcal{N}$ = 1 SYM, and the ones of even-$\textit{K}$ theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The Bethe-Ansatz approach to the $$ \mathcal{N} $$ = 4 superconformal index at finite rank

We investigate the Bethe-Ansatz approach to the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills with SU( N ) gauge group in the context of finite rank, N . We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations in recovering the exact index for N = 2 , 3. We classify the Bethe-Ansatz Equations solutions as standard (corresponding to a freely acting orbifold T 2 /Z m × Z n ) and non-standard. For N = 2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for N ≥ 3, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

79 ASTRONOMY AND ASTROPHYSICS↗