We develop a contour integral formalism for computing the K-theoretic equivariant 3-vertex. Within the Jeffrey-Kirwan (JK) residue framework, we show that, by an appropriate choice of the reference vector, both the equivariant Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) 3-vertices can be extracted from the same integrand. We analyze three distinct limits of the PT 3-vertex, recovering the unrefined topological vertex, the refined topological vertex, and the Macdonald refined topological vertex. Higher-rank extensions of PT counting and the DT/PT correspondence are also explored. From a quantum algebraic perspective, we construct an operator version of the equivariant PT 3-vertex and term it the Pandharipande-Thomas $\textit{qq}$-character. We then discuss its connection with the quantum toroidal $${\mathfrak{g}\mathfrak{l}}_{1}$$ .

France

Taro Kimura

Japan

Go Noshita

Gauge origami and quiver W-algebras. Part IV. Pandharipande-Thomas $\textit{qq}$-characters

Increasingly sensitive direct detection dark matter experiments are testing important regions of parameter space for WIMP dark matter and pushing many models to the multi-TeV regime. This brings into question the perturbativity of these models. In this context, and in light of the new limits from the LZ experiment, we investigate the status of the simplest thermal dark matter model: a singlet scalar, real or complex, coupled to the Higgs boson. We calculate the next-to-leading order (NLO) corrections to the direct detection rates as well as for the annihilations driving thermal freeze-out. For the complex case, we find that the entire perturbative region is excluded by direct detection. For the real case we find that the mass should be <math altimg='si1.svg'><mo>&#8819;</mo><mn>20</mn><mspace width='0.2em' /><mrow><mi mathvariant='normal'>TeV</mi></mrow></math> at NLO, compared with the <math altimg='si2.svg'><mo>&#8819;</mo><mn>30</mn><mspace width='0.2em' /><mrow><mi mathvariant='normal'>TeV</mi></mrow></math> LO limit. We highlight that a three-fold improvement on WIMP spin independent interactions can fully test the real scalar model in the perturbative regime. Finally, for both models, there is still an allowed (albeit narrow) region near the Higgs resonance where couplings are perturbative.

Switzerland

Miguel Escudero Abenza

Belgium

Thomas Hambye

The simplest dark matter model at the edge of perturbativity

We further develop the BPS/CFT correspondence between quiver W-algebras/ -characters and partition functions of gauge origami. We introduce -characters associated with multi-dimensional partitions with nontrivial boundary conditions which we call Donaldson-Thomas (DT) -characters. They are operator versions of the equivariant DT vertices of toric Calabi-Yau three and four-folds. Moreover, we revisit the construction of the D8 -characters with no boundary conditions and give a quantum algebraic derivation of the sign rules of the magnificent four partition function. We also show that under the proper sign rules, the D6 and D8 -characters with no boundary conditions all commute with each other and discuss its physical interpretation.

Gauge origami and quiver W-algebras. Part III. Donaldson-Thomas

We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin precession is accompanied by orbital angular momentum precession, and present examples of the resulting out-of-plane motion.

Canada

Andrzej Czarnecki

Andrei Zelnikov

Thomas precession, relativistic torque, and non-planar orbits

Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein-Hilbert gravity. Projective geometry was used long ago by Thomas et al. to succinctly package equivalent paths encoded by the geodesic equation. Projective invariance in gravity has further origins in string theory through a geometric action constructed from the method of coadjoint orbits using the Virasoro algebra. A projectively invariant connection arises from this construction, a part of which is known as the diffeomorphism field. TW gravity exploits projective Gauss-Bonnet terms in the action functional to endow the diffeomorphism field with dynamics, while allowing the theory to collapse to general relativity in the limit that the diffeomorphism field vanishes and the connection becomes Levi-Civita. In the original formulation of TW gravity, the diffeomorphism field is projectively invariant but not tensorial and the connection is projectively invariant but not affine. In this paper we reformulate TW gravity in terms of projectively invariant tensor fields and a projectively invariant covariant derivative, derive field equations respecting these symmetries, and show that the field equations obtained are classically equivalent across formulations. This provides a “Rosetta Stone” between this newly constructed covariant and projective invariant formulation of TW gravity and the original formulation that was manifestly projective invariant, but not covariant.

United States

Tyler Grover

Kory Stiffler

Patrick Vecera

Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity

The Sun may capture asymmetric dark matter (DM), which can subsequently form bound-states through the radiative emission of a sub-GeV scalar. This process enables generation of scalars without requiring DM annihilation. In addition to DM capture on nucleons, the DM-scalar coupling responsible for bound-state formation also induces capture from self-scatterings of ambient DM particles with DM particles already captured, as well as with DM bound-states formed in-situ within the Sun. This scenario is studied in detail by solving Boltzmann equations numerically and analytically. In particular, we take into consideration that the DM self-capture rates require a treatment beyond the conventional Born approximation. We show that, thanks to DM scatterings on bound-states, the number of DM particles captured increases exponentially, leading to enhanced emission of relativistic scalars through bound-state formation, whose final decay products could be observable. We explore phenomenological signatures with the example that the scalar mediator decays to neutrinos. We find that the neutrino flux emitted can be comparable to atmospheric neutrino fluxes within the range of energies below one hundred MeV. Future facilities like Hyper-K, and direct DM detection experiments can further test such scenario.

Austria

Xiaoyong Chu

Italy

Raghuveer Garani

Spain

Camilo García-Cely

CERN

Dark matter bound-state formation in the Sun

Thomas-Whitehead (TW) gravity was recently introduced as a projective gauge theory of gravity over a d-dimensional manifold that embeds reparametrization invariance into the action functional for gravitation through the use of the Thomas-Whitehead connection. The projective invariance in this d-dimensional theory enjoys an intimate relationship with the Virasoro coadjoint elements found in string theory as one of the components of the connection, <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msub></mrow></math>, is directly related to the coadjoint elements of the Virasoro algebra. TW gravity exploits projective Gauss-Bonnet terms in the action functional which allows the theory to collapse to Einstein’s theory of general relativity in the limit that <math><msub><mi>D</mi><mrow><mi>a</mi><mi>b</mi></mrow></msub></math> vanishes. In this paper we develop the graded extension of TW gravity, super-TW gravity, in the framework of a DeWitt supermanifold. We construct the Lagrangian for super-TW gravity, give a detailed derivation of the classical field equations, and discuss the graded extension of the projective connection as a prelude to a future understanding of TW-supergravity (which has manifest supersymmetry) and its relationship to the super-Virasoro algebra.

Calvin Mera Sánchez

Vincent G. J. Rodgers

Graded extension of Thomas-Whitehead gravity

We perform a systematic study of the electric and magnetic dipole moments of dark matter (DM) that are induced at the one-loop level when DM experiences four-fermion interactions with Standard Model (SM) charged fermions. Related to their loop nature these moments can largely depend on the UV completion at the origin of the four-fermion operators. We illustrate this property by considering explicitly two simple ways to generate these operators, from t- or s-channel tree-level exchange. Fixing the strength of these interactions from the DM relic density constraint, we obtain in particular a magnetic moment that, depending on the interaction considered, lies typically between 10 −20 to 10 −23 ecm or identically vanishes. These non-vanishing values induce, via photon exchange, DM-nucleus scattering cross sections that could be probed by current or near future direct detection experiments.

China

Xun-Jie Xu

Dark matter electromagnetic dipoles: the WIMP expectation

In this article we show that in the usual type-I seesaw framework, augmented solely by a neutrino portal interaction, the dark matter (DM) relic density can be created through freeze-in, in a manner fully determined by the seesaw interactions and the DM particle mass. This simple freeze-in scenario, where dark matter is not in a seesaw state, proceeds through slow, seesaw-induced decays of Higgs <math><mrow><mi>W</mi></mrow></math> and <math><mi>Z</mi></math> bosons. We identify two scenarios, one of which predicts the existence of an observable neutrino line.

Rupert Coy

Aritra Gupta

Seesaw neutrino determination of the dark matter relic density

We consider, in general terms, the possible parameter space of thermal dark matter candidates. We assume that the dark matter particle is fundamental and was in thermal equilibrium in a hidden sector with a temperature <math><msup><mi>T</mi><mo>′</mo></msup></math>, which may differ from that of the Standard Model temperature, <math><mi>T</mi></math>. The candidates lie in a region in the <math><msup><mi>T</mi><mo>′</mo></msup><mo>/</mo><mi>T</mi></math> vs. <math><msub><mi>m</mi><mrow><mi>dm</mi></mrow></msub></math> plane, which is bounded by both model-independent theoretical considerations and observational constraints. The former consists of limits from dark matter candidates that decoupled when relativistic (the relativistic floor) and from those that decoupled when nonrelativistic with the largest annihilation cross section allowed by unitarity (the unitarity wall), while the latter concerns big bang nucleosynthesis (<math><msub><mi>N</mi><mi>eff</mi></msub></math> ceiling) and free streaming. We present three simplified dark matter scenarios, demonstrating concretely how each fits into the domain.

Michel H. G. Tytgat

Laurent Vanderheyden

Domain of thermal dark matter candidates