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Rafael Herrera

Publications and source records attributed to Rafael Herrera.

At least 19 recordsLinked to original sources
arXiv2025

A topological quantum field theory for $\mathrm{Spin}(7)$-instantons

We construct a topological quantum field theory based on the moduli space of $\mathrm{Spin}(7)$-instantons on 8-dimensional manifolds. Using the Mathai-Quillen formalism, we derive the action of the theory in purely geometric terms, which coincides with prior results in the literature. We then reformulate the theory within the AKSZ formalism, obtaining a Batalin-Vilkovisky action that, after gauge fixing, matches our Mathai-Quillen construction while making the BRST symmetry explicit and providing a natural framework for classical observables. We also show that the Batalin-Vilkovisky action can be elegantly recast as a Chern-Simons type theory.

hep-th↗
arXiv2025

The High Voltage Splitter board for the JUNO SPMT system

The Jiangmen Underground Neutrino Observatory (JUNO) in southern China is designed to study neutrinos from nuclear reactors and natural sources to address fundamental questions in neutrino physics. Achieving its goals requires continuous operation over a 20-year period. The small photomultiplier tube (small PMT or SPMT) system is a subsystem within the experiment composed of 25600 3-inch PMTs and their associated readout electronics. The High Voltage Splitter (HVS) is the first board on the readout chain of the SPMT system and services the PMTs by providing high voltage for biasing and by decoupling the generated physics signal from the high-voltage bias for readout, which is then fed to the front-end board. The necessity to handle high voltage, manage a large channel count, and operate stably for 20 years imposes significant constraints on the physical design of the HVS. This paper serves as a comprehensive documentation of the HVS board: its role in the SPMT readout system, the challenges in its design, performance and reliability metrics, and the methods employed for production and quality control.

physics.ins-det↗
arXiv2021

Mass production and characterization of 3-inch PMTs for the JUNO experiment

26,000 3-inch photomultiplier tubes (PMTs) have been produced for Jiangmen Underground Neutrino Observatory (JUNO) by the Hainan Zhanchuang Photonics Technology Co., Ltd (HZC) company in China and passed all acceptance tests with only 15 tubes rejected. The mass production began in 2018 and elapsed for about 2 years at a rate of $\sim$1,000~PMTs per month. The characterization of the PMTs was performed in the factory concurrently with production as a joint effort between HZC and JUNO. Fifteen performance parameters were tracked at different sampling rates, and novel working strategies were implemented to improve quality assurance. This constitutes the largest sample of 3-inch PMTs ever produced and studied in detail to date.

physics.ins-det↗
arXiv2019

A $\mathrm{U}(2) \times \mathrm{U}(3)$ gauge theory extension of the standard model

We consider an extension of the standard model based on the group $\mathrm{U}(2) \times \mathrm{U}(3)$, which is naturally compatible with the standard model interacting-particle representations and the spontaneous symmetry breaking of $\mathrm{U}(2) \times \mathrm{U}(3)$ to an electrostrong $\mathrm{U}(3)$. In its minimal version, the model only adds one extra $\mathrm{U}(1)$ gauge boson and it implies that the hypercharge is distributed between the factors of the hyperweak and hyperstrong forces. We show that the anomaly cancellation condition can be solved by adding exotic fermions associated with a $16$-dimensional representation of $\mathrm{U}(2) \times \mathrm{U}(3)$. A brief discussion of the mechanism of the spontaneous breakdown of $\mathrm{U}(2) \times \mathrm{U}(3)$ in the gauge boson sector is given.

hep-ph↗
arXiv2019

A binary encoding of spinors and applications

We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of $Spin(8)$, explicit representations of the Lie algebras $\mathfrak{spin}(8)$, $\mathfrak{spin}(7)$ and $\mathfrak{g}_2$, etc.

math.DG↗
arXiv2019

Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles

We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also introduce the Clifford monopole equations as a natural geometric generalization of the Seiberg-Witten equations. We show that they restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit non-trivial solutions on manifolds with special Riemannian holonomy.

math.DG↗
arXiv2019

Some error estimates for the DEC method in the plane

We show that the Discrete Exterior Calculus (DEC) method can be cast as the earlier box method for the Poisson problem in the plane. Consequently, error estimates are established, proving that the DEC method is comparable to the Finite Element Method with linear elements. We also discuss some virtues, others than convergence, of the DEC method.

math.NA↗
arXiv2018

Anisotropy in 2D Discrete Exterior Calculus

We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (element by element). It also allows us to deduce, in a robust manner, anisotropic fluxes and the DEC discretization of the pullback of 1-forms by the anisotropy tensor, i.e. we deduce how the anisotropy tensor acts on primal 1-forms. Due to the local formulation, the computational cost of DEC is similar to that of the Finite Element Method with Linear interpolations functions (FEML). The numerical DEC solutions to the anisotropic Poisson equation show numerical convergence, are very close to those of FEML on fine meshes and are slightly better than those of FEML on coarse meshes.

math.NA↗
arXiv2016

Spinorially twisted Spin structures, III: CR structures

We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin$^{c, r}$ structure carrying a partially pure spinor field. We study various integrability conditions of the almost CR structure in our spinorial setup, including the classical integrability of a CR structure as well as those implied by Killing-type conditions on the partially pure spinor field. In the codimension one case, we develop a spinorial description of strictly pseudoconvex CR manifolds, metric contact manifolds and Sasakian manifolds. Finally, we study hypersurfaces of Kaehler manifolds via partially pure Spin$^c$ spinors.

math.DG↗
arXiv2015

Twisted partially pure spinors

Motivated by the relationship between orthogonal complex structures and spure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.

math.DG↗
arXiv2015

Centralizers of spin subalgebras

We determine the centralizers of certain isomorphic copies of spin subalgebras $\mathfrak{spin}(r)$ in $\mathfrak{so}(d_rm)$, where $d_r$ is the dimension of a real irreducible representation of $Cl_r^0$, the even Clifford algebra determined by the positive definite inner product on $\mathbb{R}^r$, where $r, m\in\mathbb{N}$.

math.DG↗
arXiv2015

Almost even-Clifford hermitian manifolds with large automorphism group

We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove a gap theorem for the dimension of the automorphism group.

math.DG↗
arXiv2014

A formula for the trace of symmetric powers of matrices

We present a formula for the trace of any symmetric power of a $n\times n$ matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and $n-2$ polynomial functions defined recursively.

math.DG↗