arXiv subjects

Abhishek Banerjee

Publications and source records attributed to Abhishek Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients

We obtain Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients in half-braidings for a monoidal functor. Our approach uses a formal analogy between half-braidings of a monoidal functor and the entwining of a coalgebra with an algebra. We show that the Davydov-Yetter complex with coefficients carries the structure of a weak comp algebra. In particular, it is equipped with two distinct cup product structures $\cup$ and $\sqcup$ which are related in a manner that replaces graded commutativity. By considering entwining structures in the centralizer of the monoidal functor, we introduce subcomplexes of the Davydov-Yetter complex with coefficients, which carry comp algebra structures. As a result, we obtain a graded commutative cup product and a graded Lie bracket on their cohomology which forms a Gerstenhaber algebra in the usual sense.

math.CT↗

arXiv2026

Learning Whom to Trust : Decision-Generated Credibility in Social Learning

Social interaction can improve collective learning but also amplify early mistakes. We study this tension when the credibility of social information is generated by the sender's own decision process rather than fixed ex ante. Reinforcement-learning agents make binary choices through a drift--diffusion process that jointly determines choice, decision time, and confidence; decision confidence then becomes social credibility by weighting anticipatory influence and retrospective social learning. Under balanced community exposure, the anticipatory field admits an exact quotient representation. Its local Jacobian is a scalar decision-sensitivity term multiplying the community-coupling matrix, which yields a common-mode amplification threshold and an analytical role for cross-community permeability in damping relative community differences. Monte Carlo experiments show the corresponding non-monotone performance pattern: moderate transmission accelerates correction, whereas strong transmission can lock populations into wrong consensus; low permeability instead sustains disagreement. Ablations reveal a dual role for confidence: credibility-sensitive transmission amplifies social error, while confidence-dependent private learning stabilises it. The model yields testable predictions linking sender confidence to receiver behaviour conditional on accuracy.

cs.NE↗

arXiv2026

Hochschild theory of multiplicative sequences of algebras and coalgebra measurings

We study coalgebra measurings between multiplicative sequences of algebras and the maps induced by them on Hochschild homology. The Hochschild theory of multiplicative sequences is introduced as a functor taking values in graded algebras in the symmetric monoidal category of chain complexes, constructed with the help of the shuffle product. We develop the universal measuring coalgebra, or Sweedler Hom for multiplicative sequences, as well as study several other Sweedler operations in this context. In particular, we obtain an enrichment of multiplicative sequences over cocommutative coalgebras. Using an appropriate theory of bimodules over multiplicative sequences, we study maps induced by comodule measurings on the Hochschild theory with coefficients, as well as the corresponding enriched categories. Finally, we consider measurings and generalized Sweedler operations between multiplicative sequences induced by comultiplicative sequences of coalgebras, and also the maps in Hochschild theory obtained from them.

math.RA↗

arXiv2026

Predicting the Dark Matter -- Baryon Abundance Ratio

We discuss relaxation solutions to the dark matter - baryon coincidence problem in the context of QCD axion dark matter. In relaxation solutions, a moduli dynamically adjusts the mass of dark matter and baryons until their energy densities are $\mathrm{O}(1)$ the same. Because the QCD axion is heavily connected to QCD, scanning the QCD axion mass inherently also scans the proton mass. In the context of relaxation solutions, this implies that the ratio of dark matter to baryon abundances ($Ω_{\rm DM}/Ω_{\rm B}$) is a ratio of beta functions showing that these models can only accommodate discrete values of $Ω_{\rm DM}/Ω_{\rm B}$ thereby ``predicting" the ratio of the dark matter to baryon abundances. The original composite axion model has only a single integer degree of freedom $N$, the size of the gauge group, and we show that when $N=8$ the observed value of $Ω_{\rm DM}/Ω_{\rm B} = 5.36$ is reproduced to within its percent level error bars. Novel tests of this model include more precise measurements of $Ω_{\rm DM}/Ω_{\rm B}$, a better lattice determination of the dependence of the proton mass on the high energy QCD gauge coupling, as well as more traditional tests such as fifth force experiments.

hep-ph↗

arXiv2026

Ultralight Dilatonic Dark Matter

The dilaton, a pseudo-Nambu-Goldstone boson (pNGB) of broken scale invariance, is an appealing ultralight dark matter (DM) candidate. Its mass is protected by conformal invariance and it can be searched for in tabletop experiments. However, contrary to standard pNGBs of internal symmetries, the dilaton generically has a large non-derivative self-coupling, leading to radiative contributions to its mass of the order of its decay constant. Hence typical ultralight dilatons should also have sub-eV decay constants, which would incur significant deviations from standard DM behavior at structure formation times, in severe tension with observations. Therefore, a fine-tuning is required to generate a hierarchy between the mass and the decay constant. In this work, we consider whether supersymmetry (SUSY) can be used to protect this hierarchy from quantum corrections. To ensure an ultralight dilaton mass robust against realistic SUSY-breaking contributions, we must consider a novel dilaton stabilization mechanism. The observed DM abundance can be produced by the misalignment mechanism for dilaton masses ranging from $10^{-11}$ to $1$ eV. Unfortunately, irreducible SUSY-breaking corrections due to gravity restrict the couplings between the dilaton and the Standard Model to be extremely small, beyond the reach of any current or proposed experiments. Our work demonstrates that constructing a consistent model of ultralight dilaton DM is quite involved.

hep-ph↗

arXiv2026

Coalgebra measurings, cyclic theory and homologies of matrix algebras

In this paper, we consider coalgebra measurings and the maps induced by them between Hochschild and cyclic homology of algebras. We show that these induced maps are well behaved with respect to the various structures appearing on Hochschild and cyclic homology, such as the $λ$-decomposition, the product structure, as well as the module structure of Hochschild homology over cyclic homology. Thereafter, we relate the maps between homology theories of algebras induced by a coalgebra measuring to those induced between homologies of matrix algebras. This is done in the following contexts: (a) cyclic homology and the primitive part of Lie algebra homology of the matrix algebra, (b) Hochschild homology and the primitive part of Leibniz homology of the matrix algebra, and (c) Dihedral homology of an involutive algebra and the primitive part of Lie algebra homology of symplectic or skew symmetric matrices.

math.RA↗

arXiv2026

Effect of Niobium Doping on the Crystal Structure and Hydrogen Sorption Properties of TiFe: Combined Synchrotron X-ray Diffraction and Extended X-ray Absorption Fine Structure Study

TiFe alloys are attractive compounds for solid-state stationary hydrogen storage. They can absorb hydrogen gas reversibly at near ambient temperatures and practical pressures with high volumetric capacities surpassing that of cryogenically liquified H2. The main drawback of TiFe-based storage systems is a costly activation procedure required due to the formation of oxide surface layer, which hinders hydrogen diffusion into the bulk. Doping the alloy with various additives is known to improve hydrogen diffusion softening the conditions of the activation procedure. Hydrogen sorption properties of the modified alloys have been the focus of most studies whereas less attention has been dedicated to the fundamental understanding of the effects of hydrogen sorption on the alloys' structure. The latter, however, is an important information in the knowledge-guided design of novel materials. In this work, we investigated effects of Nb-doping on crystallographic structure of TiFe metal-alloy compounds and their hydrogen sorption properties. TiFe samples with two different Nb stoichiometries were synthesized using arc-melting (AM) and characterised with synchrotron powder X-ray diffraction (SR-PXRD) and extended X-ray absorption fine structure (EXAFS) analysis. Overall, H2 absorption measurements (at 50 +/- 2 degrees C and 40 +/- 2 bar), have shown that doping of TiFe with Nb can improve matrix activation and kinetics of hydrogen sorption without compromising the overall storage capacities. Refinement of SR-PXRD and EXAFS data showed significant Nb occupancy in secondary Ti phases, which improved the hydrogenation properties of the alloys.

cond-mat.mtrl-sci↗

arXiv2026

Categorification of modules and construction of schemes

We use categorification of monoid actions to study algebraic geometry over symmetric monoidal categories. This brings together the relative algebraic geometry over symmetric monoidal categories developed by Toën and Vaquié, along with the theory of actegories over monoidal categories. We obtain schemes over a datum $(\mathcal C,\mathcal M)$, where $(\mathcal C,\otimes,1)$ is a symmetric monoidal category and $\mathcal M$ is an actegory over $\mathcal C$. One of our main tools is using the datum $(\mathcal C,\mathcal M)$ to give a Grothendieck topology on the category of affine schemes over $(\mathcal C,\otimes,1)$ that we call the ``spectral $\mathcal M$-topology.'' This consists of ``fpqc $\mathcal M$-coverings'' with certain special properties. We provide a description of schemes over $(\mathcal C,\mathcal M)$ in terms of quotients of disjoint unions of affine schemes over a certain equivalence relation. These categories of schemes are closed under pullbacks and coproducts, and are equipped with change of base functors induced by symmetric monoidal adjuctions accompanied by lax $\mathcal C$-linear functors.

math.AG↗

arXiv2025

Thermal Damping of Mass-Modulating Scalars

The cosmological evolution of a scalar field is shaped by Hubble damping. Any non-gravitational couplings of the scalar with the primordial thermal bath generically contribute additional damping. Although rarely considered, such thermal damping could be the dominant dissipative effect. We derive approximate but highly general thermal-damping rates of scalar fields that modulate the masses of thermally populated particles. We extend previous results to cover cases of particular phenomenological interest where the scalar background oscillates sinusoidally but not necessarily slowly compared to the thermalization rates of the primordial bath. Based on these results, we estimate the thermal damping of scalars coupled to neutrinos linearly, to gluons quadratically, and to WIMPs linearly, and demonstrate its importance in certain parameter space of these models. We also estimate the thermal damping rates in models of QCD axion.

hep-ph↗

arXiv2025

Oscillating nuclear charge radii as sensors for ultralight dark matter

We show that coupling of ultralight dark matter (UDM) to quarks and gluons would lead to an oscillation of the nuclear charge radius for both the quantum chromodynamics (QCD) axion and scalar dark matter. Consequently, the resulting oscillation of electronic energy levels could be resolved with optical atomic clocks, and their comparisons can be used to investigate UDM-nuclear couplings, which were previously only accessible with other platforms. We demonstrate this idea using the ${}^2S_{1/2} (F=0)\leftrightarrow {}^2F_{7/2} (F=3)$ electric octupole and ${}^2S_{1/2} (F=0)\leftrightarrow \,{}^2D_{3/2} (F=2)$ electric quadrupole transitions in ${}^{171}Yb^+$. Based on the derived sensitivity coefficients for these two transitions and a long-term comparison of their frequencies using a single trapped ${}^{171}Yb^+$ ion, we find bounds on the scalar UDM-nuclear couplings and the QCD axion decay constant. These results are at a similar level compared to the tightest spectroscopic limits, and future investigations, also with other optical clocks, promise significant improvements.

hep-ph↗

arXiv2025

Rydberg Single Photon Detection for Probing 0.1-10 meV Dark Matter with BREAD

We introduce a Rydberg-based single photon detector (SPD) for probing dark matter in the 0.1-10 meV mass range (20 GHz-2 THz). The Rydberg SPD absorbs photons produced and focused by the BREAD dish antenna and trades them for free, detectable electrons. At the lower end of the mass range, photons drive Rydberg-Rydberg transitions, which are read out via state-selective ionization. At higher masses, they directly ionize the Rydberg atoms.

hep-ph↗

arXiv2025

Thermal Damping of Neutrino-Coupled Scalar Dark Matter

We point out that ultralight scalar dark matter that modulates neutrino masses can be significantly thermal damped by cosmic neutrinos in the early universe. This dissipative effect arises as a backreaction from the neutrinos which are being driven slightly out of thermal equilibrium by the scalar. We estimate the rate of such thermal damping and explore its phenomenological implications. For a scalar that is produced early, we find that the effect of thermal damping results in a predictable final abundance largely insensitive to its initial condition while circumventing late time limits. This motivates a parameter-space line to target experimentally.

hep-ph↗

arXiv2025

Searching for hadronic scale baryonic and dark forces at $(g-2)_μ$'s lattice-vs-dispersion front

The anomalous magnetic moment of the muon ($\,a_μ\,$) provides a stringent test of the quantum nature of the Standard Model (SM) and its extensions. To probe beyond the SM physics, one needs to be able to subtract the SM contributions, which consists of a non-perturbative part, namely, the hadronic vacuum polarization (HVP) of the photon. The state of the art is to predominantly use two different methods to extract this HVP: lattice computation, and dispersion relation-based, data-driven method. Thus one can construct different forms of the ``$a_μ$ test" which compares the precise measurement of $a_μ$ to its theory prediction. Additionally, this opens the possibility for another subtle test, where these two ``theory" predictions themselves are compared against each other, which is denoted as the ``HVP-test". This test is particularly sensitive to hadronic scale new physics. Therefore, in this work, we consider a SM extension consisting of a generic, light $\sim(100~{\rm MeV}-1~{\rm GeV})$ vector boson and study its impact on both tests. We develop a comprehensive formalism for this purpose. We find that in the case of data-driven HVP being used in the $a_μ$ test, the new physics contributions effectively cancels for a flavor-universal vector boson. As an illustration of these general results, we consider two benchmark models: i)~the dark photon ($\,A'\,$) and ii)~a gauge boson coupled to baryon-number ($\,B\,$). Using a combination of these tests, we are able to constrain the parameter space of $B$ and $A'$, complementarily to the existing limits. As a spin-off, our preliminary analysis of the spectrum of invariant mass of $3π$ in events with ISR at the $B-$ factories (BaBar, Belle) manifests the value of such a study in searching for $B\to 3π$ decay, thus motivating a dedicated search by experimental collaborations.

hep-ph↗

arXiv2025

Eilenberg-Moore categories and quiver representations of monads and comonads

We consider representations of quivers taking values in monads or comonads over a Grothendieck category $\mathcal C$. We treat these as scheme like objects whose ``structure sheaf'' consists of monads or comonads. By using systems of adjoint functors between Eilenberg-Moore categories, we obtain a categorical framework of modules over monad quivers, and of comodules over comonad quivers. Our main objective is to give conditions for these to be Grothendieck categories, which play the role of noncommutative spaces. As with usual ringed spaces, we have to study two kinds of module categories over a monad quiver. The first behaves like a sheaf of modules over a ringed space. The second consists of modules that are cartesian, which resemble quasi-coherent sheaves. We also obtain an extension of the classical quasi-coherator construction to modules over a monad quiver with values in Eilenberg-Moore categories. We establish similar results for comodules over a comonad quiver. One of our key steps is finding a modulus like bound for an endofunctor $U:\mathcal C\longrightarrow \mathcal C$ in terms of $κ(G)$, where $G$ is a generator for $\mathcal C$ and $κ(G)$ is a cardinal such that $G$ is $κ(G)$-presentable. Another feature of our paper is that we study modules over a monad quiver in two different orientations, which we refer to as ``cis-modules'' and ``trans-modules.'' We conclude with rational pairings of a monad quiver with a comonad quiver, which relate comodules over a comonad quiver to coreflective subcategories of modules over monad quivers.

math.CT↗

arXiv2025

Stacking the Deck: Gambling on a Light QCD Axion

We consider axions lighter than what their QCD couplings might otherwise suggest. Starting with a $\mathbb{Z}_N$-axion, we introduce a small explicit $\mathbb{Z}_N$ symmetry-breaking coupling between the Standard Model Higgs boson and a reheaton. This small explicit breaking allows us to populate a large portion of the light axion $m_a$-$f_a$ plane, removes the $1/N$ tuning in the $\mathbb{Z}_N$-axion, and explains why only our sector was reheated. Due to finite temperature effects, axions of this sort undergo either ``rigged" misalignment, where the axion misalignment angle is effectively $π$ regardless of its initial value; or ``shuffled" misalignment, where the initial angle is effectively randomized.

hep-ph↗

arXiv2025

A note on measurings and higher order Hochschild homology of algebras

We know that coalgebra measurings behave like generalized maps between algebras. In this note, we show that coalgebra measurings between commutative algebras induce morphisms between higher order Hochschild homology groups of algebras. By higher order Hochschild homology, we mean the the Hochschild homology groups of a commutative algebra with respect to a simplicial set as introduced by Pirashvili.

math.RA↗

arXiv2025

Galois measurings for noncommutative base change of entwined contramodule and entwined comodule categories

We study the noncommutative base change of an entwining structure $(A,C,ψ)$ by a Grothendieck category $\mathfrak S$, using two module like categories. These are the categories of entwined comodule objects and entwined contramodule objects in $\mathfrak S$ over the entwining structure $(A,C,ψ)$. We consider criteria for maps between these noncommutative spaces, induced by generalized maps between entwining structures, known as measurings, to behave like Galois extensions. We also study conditions for extensions of these noncommutative spaces, understood as functors between module like categories, to have separability, Frobenius or Maschke type properties.

math.RA↗

arXiv2025

Momentum and Matter Matter for Axion Dark Matter Matters on Earth

We investigate the implications of matter effects to searches for axion Dark Matter on Earth. The finite momentum of axion Dark Matter is crucial to elucidating the effects of Earth on both the axion Dark Matter field value and its gradient. We find that experiments targeting axion couplings compatible with canonical solutions of the strong CP puzzle are likely not affected by Earth's matter effects. However, experiments sensitive to lighter axions with stronger couplings can be significantly affected, with a significant part of the parameter space suffering from a reduced axion field value, and therefore decreased experimental sensitivity. In contrast, the spatial gradient of the axion field can be enhanced along Earth's radial direction, with important implications for ongoing and planned experiments searching for axion Dark Matter.

hep-ph↗