arXiv subjects

A. Sierra-Martínez

Publications and source records attributed to A. Sierra-Martínez.

3 recordsLinked to original sources

arXiv2026

Batalin-Vilkovisky description of Yang-Mills theories with universal extra dimensions

The Batalin-Vilkovisky (BV) framework is a powerful technique for quantizing a wide range of gauge systems. This formalism employs fields and antifields--introducing a symplectic structure through the antibracket--to implement BRST symmetry, which captures the essence of gauge invariance. Within this context, we study the symmetry structure of a pure Yang-Mills theory with universal extra dimensions. We construct a BRST-invariant extended action for the $(4+n)$-dimensional theory depending on fields and antifields, which constitutes a proper solution to the master equation. The higher-dimensional spacetime and gauge symmetries are then hidden within their four-dimensional counterparts via canonical transformations. Gauge invariances are fixed by combining gauge-fixing procedures for both the standard and Kaluza-Klein (KK) fields. This procedure is implemented covariantly in the adjoint representation of the gauge group. While the standard gauge fields are fixed using the Background Field Method (BFM), the KK gauge excitations are fixed covariantly, as they transform as matter fields. Finally, the manifest $SU(N)$ gauge symmetry of the quantized theory is emphasized.

hep-th↗

arXiv2025

Gauge structure of Yang-Mills theories with extra dimensions

An effective Lagrangian for Yang-Mills theories with $n$ extra dimensions is constructed. We start from a field theory governed by the extra-dimensional Poincaré group $ISO(1,3+n)$ and the extended gauge group $SU(N,M^{4+n})$, characterized by an energy scale $Λ$ and assumed to be valid at energies far below this scale. Assuming that the size of the extra dimensions is much larger than the distance scale at which this theory is valid, an effective theory with symmetry groups $ISO(1,3)$ and $SU(N,M^{4})$ is constructed. Such theories are connected by a canonical transformation that hides $ISO(1,3+n)\otimes SU(N,M^{4+n})$ into $ISO(1,3)\otimes SU(N,M^{4})$, and endows the KK gauge fields with mass. Using a set of orthogonal functions $\{f^{(\underline{0})},f^{(\underline{m})}(\bar x)\}$, generated by the Casimir invariant $\bar{P}^2$ associated with the translations subgroup $T(n)\subset ISO(n)$, the degrees of freedom of $ISO(1,3+n)\otimes SU(N,M^{4+n})$ are expanded via a general Fourier series, whose coefficients are the degrees of freedom of $ISO(1,3)\otimes SU(N,M^{4})$. These functions, corresponding to the projection on the coordinates basis $\{|\bar{x} \big >\}$ of the discrete basis $\{|0\big >,|p^{(\underline{m})}\big >\}$ generated by $\bar {P}^2$, are central in defining the effective theory. Components along the base state $f^{(\underline{0})}=\big <\bar x|0\big>$, identified as the standard Yang-Mills fields, do not receive mass at the compactification scale; components along excited states $f^{(\underline{m})}=\big <\bar x|p^{(\underline{m})}\big>$, corresponding to KK excitations, receive mass at this scale. Associated with any direction $|p^{(\underline{m})}\neq0\big >$ there are a massive gauge field and a pseudo-Goldstone boson. Resemblances of this mass-generating mechanism with the Brout-Englert-Higgs mechanism are stressed.

hep-ph↗

arXiv2020

Implications of extra dimensions on the effective charge and the beta function in quantum electrodynamics

A comprehensive analysis on the photon self-energy, the fermion self-energy, and the fermion vertex function is presented at one loop in the context of quantum electrodynamics (QED) with 1 extra dimension. In 5-dimensional theories, characterized by an infinite number of Kaluza-Klein fields, one-loop amplitudes involve discrete as well as continuous sums, $\sum^\infty_{n=1}\int d^4k$, that could diverge. Using dimensional regularization, we express such sums as products of gamma and Epstein functions, both defined on the complex plane, with divergences arising from poles of these functions in the limit as $ D \to 4$. Using the analytical properties of the Epstein function, we show that the ultraviolet divergences generated by the Kaluza-Klein sums can be consistently renormalized, which means that the corresponding renormalized quantities reduce to the usual ones of QED at the limit of a very large compactification scale $R^{-1}$. The main features of QED at the one-loop level were studied. We use the mass-dependent $μ$-scheme to calculate, in QED with an arbitrary number $n$ of extra dimensions, a beta function fulfilling all desirable physical requirements. We argue that in this type of theories, with a large mass spectrum covering a wide energy range, beta functions should not be calculated by using mass-independent renormalization schemes. We show that the beta function is finite for any energy $μ$. In particular, it reduces to the usual QED result $e^3/12π^2$ for $m\ll μ\ll R^{-1}$ and vanishes for $m\gg μ$, with $m$ the usual fermion mass. Throughout the work, the decoupling nature of all our results obtained from the analytical properties of the Epstein function is stressed.

hep-ph↗