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DOE OSTI2022

Celestial operator product expansions and w 1+∞ symmetry for all spins

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w 1+∞ . In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w 1+∞ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Renormalization group improved photon impact factors and the high energy virtual photon scattering

We perform the renormalization group improved collinear resummation of the photon-gluon impact factors. We construct the resummed cross section for virtual photon-photon (γ ∗ γ ∗ ) scattering which incorporates the impact factors and BFKL gluon Green’s function up to the next-to-leading logarithmic accuracy in energy. The impact factors include important kinematical effects which are responsible for the most singular poles in Mellin space at next-to-leading order. Further conditions on the resummed cross section are obtained by requiring the consistency with the collinear limits. Our analysis is consistent with previous impact factor calculations at NLO, apart from a new term proportional to C F that we find for the longitudinal polarization. Finally, we use the resummed cross section to compare with the LEP data on the γ ∗ γ ∗ cross section and with previous calculations. The resummed result is lower than the leading logarithmic approximation but higher than the pure next-to-leading one, and is consistent with the experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Strong coupling expansion for the conformal Pomeron/Odderon trajectories

From the perspective of AdS/CFT the Pomeron is identified with a Reggeized Graviton, while the Odderons correspond to Reggeized anti-symmetric AdS 5 Kalb-Ramond tensor-fields. In this paper, we consider the strong coupling expansion of the dimension of the leading twist operators dual to these Regge trajectories, Δ(j), to determine its analytic continuation in j beyond the diffusion limit. In particular, we compute the strong coupling expansion of the intercept to order λ -3 , where λ is the t’Hooft coupling, for both the Pomeron, which is C = +1 crossing-even, and the “Odderons”, which are the leading C = -1 crossing-odd Regge singularities. We discuss the spectral curves of the class of single-trace operators to which these string modes couple.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Fermionic Glauber operators and quark reggeization

We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the t-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in |t|/s relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as $q\overline{q}$→ $gg$ and $q\overline{q}$→$γγ$. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the 3 color channel, as well as the leading logarithmic BFKL equation. Results in the $\overline{6}$ and 15 color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Gluon transverse-momentum-dependent distributions from large-momentum effective theory

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the $\overline{MS}$ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for the extraction of gluon TMDPDFs from lattice simulations, and have the potential to greatly facilitate perturbative calculations of the hard matching kernel.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Integrable field theories and their CCFT duals

We compute the Mellin transforms of various two-dimensional integrable S-matrices, providing the first explicit, non-perturbative realizations of celestial CFT. In two dimensions, the Mellin transform is simply the Fourier transform in rapidity space, and the “celestial correlator” has no position dependence. The simplified setting allows us to study the analytic properties of CCFT correlators exactly as a function of the conformal dimensions. We find that the correlators exist as real distributions of the conformal weights, with asymptotics controlled by the mass spectrum and three-point couplings of the model. Coupling these models to a flat space limit of JT gravity preserves integrability and dresses the amplitudes by a rapidly varying gravitational phase. We find that the coupling to gravity smooths out certain singular aspects of the Mellin-transformed correlators.

2D Gravity↗

DOE OSTI2023

The reflected entanglement spectrum for free fermions

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Thermal energy of a charm-meson molecule in a pion gas

The thermal corrections to the propagator of a loosely bound charm-meson molecule in a pion gas are calculated to next-to-leading order in the heavy-meson expansion using a zero-range effective field theory. Ultraviolet divergences in the charm-meson-pair self energy are canceled by corrections to the charm-meson-pair contact vertex. Terms that are singular at the charm-meson-pair threshold can be absorbed into thermal corrections to the rest energies and kinetic masses of the charm-meson constituents. The remaining terms reduce to a thermal correction to the binding momentum that is proportional to the pion number density and suppressed by the pion/charm-meson mass ratio. The correction gives a tiny decrease in the binding energy of the charm-meson molecule relative to the charm-meson-pair threshold in the pion gas and a change in its thermal width that is small compared to the thermal widths of the charm-meson constituents. These results are encouraging for the prospects of observing X(3872) and $T$$^{+}_{cc}$ (3875) in the expanding hadron gas produced by heavy-ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Anatomy of the amplituhedron

We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar $ \mathcal{N}=4 $ SYM theory. We do so by introducing and studying its stratification, focusing on four-point amplitudes. The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations. As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries. We recover the stratifications of some of these geometries from the singularities of the corresponding integrands, providing a non-trivial test of the amplituhedron/scattering amplitude correspondence. We finally introduce a deformation of the stratification with remarkably simple topological properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Ubiquity of non-geometry in heterotic compactifications

Here, we study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest nontrivial elliptic fibration the effect is quite dramatic: the I 1 degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the T 2 . This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety due to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

The two-loop five-point amplitude in $\mathcal{N}$ = 8 supergravity

We compute the symbol of the two-loop five-point amplitude in $\mathcal{N}$ = 8 supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also d-dimensional ones, as the former are insufficient. Our novel d-dimensional unitarity-based approach to the systematic construction of an amplitude’s rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $\mathcal{N}$ = 8 supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $\mathcal{N}$ = 4 super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $\mathcal{N}$ = 4 super-Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Fibers add flavor. Part II. 5d SCFTs, gauge theories, and dualities

In [1, 2] we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $$ \mathcal{N} $$ N = (1 , 0) SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi-Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Complement to thermodynamics of dyonic Taub-NUT-AdS spacetime

We examine the thermodynamics of Euclidean dyonic Taub-Nut/Bolt-AdS 4 black holes for a variety of horizon geometries to understand how gauge field regularity conditions influence the thermodynamic relations. We find several distinct features that distinguish the NUT-charged case from its dyonic Reissner-Nordstrom counterpart. For the Nut solution, the gauge field vanishes at the horizon and so regularity is ensured. For the Bolt solution we find that the norm of the gauge field is required to vanish at the horizon in order to satisfy both regularity and the first law of thermodynamics. This regularity condition yields a constraint on the electric and magnetic charges and so reduces cohomogeneity of the system; for spherical horizons, the regularity condition removing the Misner string singularity further reduces cohomogeneity. We observe that bolt solutions with increasing electric charge have positive heat capacity, but upon turning on the magnetic charge to make the solution dyonic, we find that the properties of the uncharged one are retained, having both positive and negative heat capacity. We also study the extremal Bolt solution, finding that Misner string disappears at the horizon in the zero temperature limit. We find that the extremal solution has finite-temperature-like behaviour, with the electric potential playing a role similar to temperature.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Integrands of less-supersymmetric Yang-Mills at one loop

We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric (1 ≤ $\mathcal{N}$ ≤ 4) Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV. The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Exact WKB and the quantum Seiberg-Witten curve for 4d $N$ = 2 pure SU(3) Yang-Mills. Abelianization

We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on $\mathbb{CP}^1$ with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,$\mathbb{C}$)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Exact quantization and analytic continuation

In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Love symmetry in higher-dimensional rotating black hole spacetimes

We develop a method for constructing a 1-parameter family of globally-defined Love symmetry generators in rotating black hole spacetimes of general dimension. The key ingredient is to focus on the vicinity of the (physical) outer horizon, matching only the radial derivative and the outer horizon pole pieces of the Klein-Gordon operator in the black hole spacetime to the SL(2, ℝ) Casimir operator. After revisiting the 4D Kerr and 5D Myers-Perry cases, the procedure is illustrated on generalized Lense-Thirring spacetimes which describe a wide variety of slowly rotating black hole metrics in any number of dimensions. Such spacetimes are known to admit an extended tower of Killing tensor and Killing vector symmetries and, as demonstrated in this paper, allow for separability of the massive scalar wave equation in Myers-Perry-like coordinates. Interestingly, separability also occurs in the horizon-penetrating Painlevé–Gullstrand coordinates associated with the freely infalling observer who registers flat space around her all the way to singularity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

M5 brane and four dimensional $ \mathcal{N} $ = 1 theories I

Four dimensional N=1 theories are engineered by compactifying six dimensional (2,0) theory on a Riemann surface with regular punctures. A generalized Hitchin's equation involving two Higgs fields is proposed as the BPS equation for N=1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is described by rotating branes representing N=2 puncture. As an application, we show that the Seiberg duality of SU(N) SQCD with N f =2N and certain superpotential term is realized as different degeneration limits of the same punctured Riemann surface, and also find four more dual theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗