Related papers: Complete Operator Basis for the modular invariant …
Let W be an affine variety equipped with an action of a reductive group G. The invariant Hilbert scheme is a moduli space which classifies the G-stable closed subschemes of W such that the affine algebra is the direct sum of simple…
We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form…
We propose an interesting assignment of positive modular wights for fields in a modular non-Abelian discrete flavor symmetry. By this assignment, we can construct inverse seesaw and linear seesaw models without any additional symmetries…
The persistent anomalies observed in $b \to s\,(\ell^+\ell^-,\,\nu\bar{\nu})$ transitions continue to provide strong motivation for exploring possible extensions of the Standard Model (SM). Motivated by these discrepancies, we present a…
We study the vacuum geometry prescribed by the gauge invariant operators of the MSSM via the Plethystic Programme. This is achieved by using several tricks to perform the highly computationally challenging Molien-Weyl integral, from which…
The Standard Model Effective Field Theory (SMEFT) offers a systematic approach to study potential deviations from the Standard Model (SM) through higher-dimensional operators that encapsulate new physics effects. In this work, we analyze…
We present an efficient algorithm for determining the Hilbert series of an effective theory and provide a companion code called ECO (Efficient Counting of Operators) in FORM. For example, the Hilbert series for the dimension 15 operators in…
We obtain SMEFT bounds using an approach that utilises the complete multi-dimensional differential information of a process. This approach is based on the fact that at a given EFT order, the full angular distribution in the most important…
We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any…
We propose to generate the flavor structures of the Standard Model plus neutrinos from flipped SU(5) GUT with $A_4$ modular flavor symmetry. Possible way to assign different moduli values for quarks and leptons in modular GUT scheme is…
An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinite-dimensional Hubbard model is developed on the basis of a…
In this paper, we propose methods for computing the Hilbert series of multigraded right modules over the free associative algebra. In particular, we compute such series for noncommutative multigraded algebras. Using results from the theory…
We present the explicit construction of the effective field theory (EFT) of standard model mass eigenstates. The EFT, which is invariant under $U(1)_{\text{e.m.}}\times SU(3)_c$, is constructed based on the on-shell method and Young Tableau…
We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients…
Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a $\mathbb{Z}_4$ symmetry provided there exists a basis of operators in the QFT where all operators have even operator dimension, $d$,…
Theoretical interpretations of particle physics data, such as the determination of the Wilson coefficients of the Standard Model Effective Field Theory (SMEFT), often involve the inference of multiple parameters from a global dataset.…
We carry out a thorough study of weight-shifting operators on Hilbert modular forms in characteristic $p$, generalizing the author's prior work with Sasaki to the case where $p$ is ramified in the totally real field $F$. In particular we…
We develop two approaches to Quantum (or Non-commutative) Graphs based on arbitrary von Neumann algebras $M\subseteq\mathcal B(H)$: one looking at operator bimodules of Hilbert--Schmidt (instead of bounded) operators, and the second looking…
We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$-theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we…
Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the…