Local Gauge Theory Research Articles

Presymplectic minimal models of local gauge theories

Presymplectic minimal models of local gauge theories

Asymptotic symmetries of gravity in the gauge PDE approach

We propose a framework to study local gauge theories on manifolds with boundaries and their asymptotic symmetries, which is based on representing them as so-called gauge PDEs. These objects extend the conventional BV-AKSZ sigma-models to the case of not necessarily topological and diffeomorphism invariant systems and are known to behave well when restricted to submanifolds and boundaries. We introduce the notion of gauge PDE with boundaries, which takes into account generic boundary conditions, and apply the framework to asymptotically flat gravity. In so doing, we start with a suitable representation of gravity as a gauge PDE with boundaries, which implements the Penrose description of asymptotically simple spacetimes. We then derive the minimal model of the gauge PDE induced on the boundary and observe that it provides the Cartan (frame-like) description of a (curved) conformal Carollian structure on the boundary. Furthermore, imposing a version of the familiar boundary conditions in the induced boundary gauge PDE, leads immediately to the conventional Bondi–Metzner–Sachs algebra of asymptotic symmetries. Finally, we briefly sketch the construction for asymptotically (A)dS gravity.

Notes on the L∞-approach to local gauge field theories

It is well known that a Q-manifold gives rise to an L∞-algebra structure on the tangent space at a fixed point of the homological vector field. From the field theory perspective this implies that the expansion of a classical Batalin-Vilkovisky (BV) formulation around a vacuum solution can be equivalently cast into the form of an L∞-algebra. In so doing, the BV symplectic structure determines a compatible cyclic structure on the L∞-algebra. Moreover, L∞ quasi-isomorphisms correspond to so-called equivalent reductions (also known as the elimination of generalized auxiliary fields) of the respective BV systems. Although at the formal level the relation is straightforward, its implementation in field theory requires some care because the underlying spaces become infinite-dimensional. In the case of local gauge theories, the relevant spaces can be approximated by nearly finite-dimensional ones through employing the jet-bundle technique. In this work we study the L∞-counterpart of the jet-bundle BV approach and generalise it to a more flexible setup of so-called gauge PDEs. It turns out that in the latter case the underlying L∞-structure is analogous to that of Chern-Simons theory. In particular, the underlying linear space is a module over the space-time exterior algebra and the higher L∞-maps are multilinear. Furthermore, a counterpart of the cyclic structure turns out to be degenerate and possibly nonlinear, and corresponds to a compatible presymplectic structure the gauge PDE, which is known to encode the BV symplectic structure and hence the full-scale Lagrangian BV formulation. Moreover, given a degenerate cyclic structure one can consistently relax the L∞-axioms in such a way that the formalism still describes non-topological models but involves only finitely-generated modules, as we illustrate in the example of Yang-Mills theory.

Presymplectic BV-AKSZ formulation of conformal gravity

We elaborate on the presymplectic BV-AKSZ approach to local gauge theories and apply it to conformal gravity. More specifically, we identify a compatible presymplectic structure on the minimal model of the total BRST complex of this theory and show that together with the BRST differential it determines a full-scale BV formulation for a specific frame-like action which seems to be previously unknown. Remarkably, the underlying frame-like description requires no artificial off-shell constraints. Instead, the action becomes equivalent to the usual conformal gravity one, upon gauging away all the variables belonging to the kernel of the presymplectic structure. Finally, we show how the presymplectic BV-AKSZ approach extends to generic gauge theories.

Presymplectic AKSZ formulation of Einstein gravity

Any local gauge theory can be represented as an AKSZ sigma model (upon parameterization if necessary). However, for non-topological models in dimension higher than 1 the target space is necessarily infinite-dimensional. The interesting alternative known for some time is to allow for degenerate presymplectic structure in the target space. This leads to a very concise AKSZ-like representation for frame-like Lagrangians of gauge systems. In this work we concentrate on Einstein gravity and show that not only the Lagrangian but also the full-scale Batalin-Vilkovisky (BV) formulation is naturally encoded in the presymplectic AKSZ formulation, giving an elegant supergeometrical construction of BV for Cartan-Weyl action. The same applies to the main structures of the respective Hamiltonian BFV formulation.

Nonrelativistic open string and Yang-Mills theory

The classical and quantum worldsheet theory describing nonrelativistic open string theory in an arbitrary nonrelativistic open and closed string background is constructed. We show that the low energy dynamics of open strings ending on n coincident D-branes in flat spacetime is described by a Galilean invariant U(n) Yang-Mills theory. We also study nonrelativistic open string excitations with winding number and demonstrate that their dynamics can be encoded into a local gauge theory in one higher dimension. By demanding conformal invariance of the boundary couplings, the nonlinear equations of motion that govern the consistent open string backgrounds coupled to an arbitrary closed background (described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field) are derived and shown to emerge from a Galilean invariant Dirac-Born-Infeld type action.

Geometric unification of Higgs bundle vacua

Higgs bundles are a central tool used to study a range of intersecting brane systems in string compactifications. Solutions to the internal gauge theory equations of motion for the corresponding worldvolume theories of branes give rise to different low energy effective field theories. This has been heavily used in the study of M-theory on local $G_2$ spaces and F-theory on local elliptically fibered Calabi-Yau fourfolds. In this paper we show that the 3D $\mathcal{N} = 1$ effective field theory defined by M-theory on a local $Spin(7)$ space unifies the Higgs bundle data associated with 4D $\mathcal{N} = 1$ M- and F-theory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of M-theory on such local $Spin(7)$ spaces, and build explicit interpolating solutions. This provides a complementary local gauge theory analysis of a recently proposed approach to constructing $Spin(7)$ spaces from generalized connected sums.

Gravity: local or nonlocal

While gravity is often imagined to have the characteristics of a local gauge theory, no such gauge theory has so far been constructed, with all attempts at quantum gravity leading to nonrenormalizable infinities. All known gauge theories, however, have both local and nonlocal aspects, and it is worth exploring how far we can describe gravity using a nonlocal starting point. It is suggested that this leads to a local theory which privileges inertia rather than gravity. Such a theory based on a repulsive force, would be renormalizable, and it would also have consequences that can be linked to cosmological redshift, dark energy and possibly also dark matter. It further suggests generic connections between gravity and inertia and between general relativity and Newtonian gravity.

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Compact nonlocal Abelian gauge theory in (2 + 1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large NF limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3 + 1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus {mathbbm{T}}_3 . Analogous results for the S2 × S1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.

Obtaining consistent Lorentz gauging for a gravitationally coupled fermion

For internal gauge forces, the result of locally gauging, i.e., of performing the substitution $\partial \rightarrow D$, is physically the same whether performed on the action or on the corresponding Euler-Lagrange equations of motion. Rather unsettling, though, such commutativity fails for the standard way of coupling a Dirac fermion to the gravitational field in the setting of a local Lorentz gauge theory of general relativity in the vierbein formalism, the equivalence principle thus seemingly being here violated. This paper will present a formalism in which commutativity holds for the gravitational force as well, the action for the gravitational field itself being still the Einstein-Hilbert one. Notably, in this formalism, the spinor field will carry a world/coordinate index, rather than a Lorentz spinor index as it does standardly. More generally, no Lorentz indices will figure, neither vector indices nor spinor indices, which from a parsimonious point of view seems quite satisfactory.

Gauging the boundary in field-space

Local gauge theories are in a complicated relationship with boundaries. Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements. Therefore, coupling is inimical to gauge-fixing, as usually understood. This resistance to gauge-fixing has led some to declare the coupling of subsystems to be the raison d’être of gauge (Rovelli, 2014).Indeed, while gauge-fixing is entirely unproblematic for a single region without boundary, it introduces arbitrary boundary conditions on the gauge degrees of freedom themselves—these conditions lack a physical interpretation when they are not functionals of the original fields. Such arbitrary boundary choices creep into the calculation of charges through Noether's second theorem (Noether, 1971), muddling the assignment of physical charges to local gauge symmetries. The confusion brewn by gauge at boundaries is well-known, and must be contended with both conceptually and technically.It may seem natural to replace the arbitrary boundary choice with new degrees of freedom, for using such a device we resolve some of these confusions while leaving no gauge-dependence on the computation of Noether charges (Donnelly & Freidel, 2016). But, concretely, such boundary degrees of freedom are rather arbitrary—they have no relation to the original field-content of the field theory. How should we conceive of them?Here I will explicate the problems mentioned above and illustrate a possible resolution: in a recent series of papers (Gomes, Hopfmller,& Riello, 2018; Gomes & Riello, 2017, 2018) the notion of a connection-form was put forward and implemented in the field-space of gauge theories. Using this tool, a modified version of symplectic geometry—here called ‘horizontal’—is possible. Independently of boundary conditions, this formalism bestows to each region a physically salient, relational notion of charge: the horizontal Noether charge. Meanwhile, as required, the connection-form mediates a composition of regions, one compatible with the attribution of horizontal Noether charges to each region. The aims of this paper are to highlight the boundary issues in the treatment of gauge, and to discuss how gauge theory may be conceptually clarified in light of a resolution to these issues.

Mass splittings in a linear sigma model for multiflavor gauge theories

We calculate the tree-level mass spectrum for a linear sigma model describing the scalar and pseudoscalar mesons of a $SU(3)$ local gauge theory with Dirac fermions in the fundamental representation. $N_1$ fermions have a mass $m_1$ and $N_2$ a mass $m_2$. Using recent lattice data with $m_1=m_2$ and $N_1+N_2$= 8 or 12, we predict the mass splittings for $m_2=m_1+\delta m$. At first order in $\delta m$, an interesting inverted pattern appears in the $0^{++}$ sector, where mesons with lighter fermions are heavier. This feature could be tested in ongoing calculations provided that $m_1$ and $\delta m$ are sufficiently small. We discuss possible improvements of the approach.

On the Brout–Englert–Higgs–Guralnik–Hagen–Kibble Mechanism in Quantum Gravity

Local gauge invariance can materialise in different ways in theories for quantised elementary particles. It is less well-known, however, that a quite similar situation also occurs in the Einstein–Hilbert formalism for the gravitational forces. This may have important consequences for quantum theory. At first sight one may even think that it renders gravity renormalisable, just as happens in local gauge theories, but in gravity the truth is more puzzling.

Linear sigma model for multiflavor gauge theories

We consider a linear sigma model describing $2N_f^2$ bosons ($\sigma$, ${\bf a_0}$, $\eta '$ and ${\bf \pi}$) as an approximate effective theory for a $SU(3)$ local gauge theory with $N_f$ Dirac fermions in the fundamental representation. The model has a renormalizable $U(N_f)_L\bigotimes U(N_f)_R$ invariant part, which has an approximate $O(2N_f^2)$ symmetry, and two additional terms, one describing the effects of a $SU(N_f)_V$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $N_f$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $N_f$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $M_\sigma^2\simeq (2/N_f-C_\sigma)M_{\eta '}^2$ should apply in the chiral limit. Lattice measurements of $M_{\eta '}^2$ and of approximate constants such as $C_\sigma$ could help locating the boundary of the conformal window. We show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.

E(2) gauge theory model of effective gravitational theory at large scale

At the cosmological scale, there exist many anisotropic anomalies in the low-l multipoles of the CMB angular power spectrum. Especially, the normals to the octopole and quadrupole planes are aligned with the direction of the cosmological dipole at a level inconsistent with Gaussian random. The inconsistency indicates that the anomalies may not be boost effect from the CMB rest frame to the peculiar frame. It hints us that the boost invariance might be violated on a cosmological scale. There are some discrepancies between the astronomical and cosmological observations, and the predictions are solely based on general relativity and the standard model for elementary particle physics. The solutions are the introduction of dark matter and dark energy. However, all the experiments aiming at finding dark matter particles give negative result and it is still a mystery:what the dark energy is comprised of. We suppose that the Lorentz symmetry begins to be violated partly from the scale of galaxy and utilize the very special relativity symmetry group E(2) as an example to illustrate the Lorentz violation effect on the large-scale effective gravity. A local E(2) but Lorentz invariant gauge theory can be constructed based on the equivalence principle and the gauge principle. To realize the E(2) symmetry, the closure requirement of Maurer-Cartan eqnarray on E(2) algebra needs to be satisfied by postulating constraint conditions among the components of the Lorentz connection. The local Lorentz invariant gauge theory with a Hilbert-Einstein action is a theory with torsion in general case. However in the case of scalar matter source, the theory is exactly the theory of general relativity with Levi-Civita connection and zero torsion. In the E(2) gauge theory case, the closure requirement of Maurer-Cartan eqnarray for E(2) algebra postulates 12 constraint eqnarrays among the components of the Lorentz connection and the eqnarrays of motion for connection reduce the number of independent components of connection to 12. The eqnarrays of motion for the tetrad field do not contain only the involved tetrad field components nor these relevant independent components. So the whole number of variables needed to be solved is 12 more than that in general relativity while there are 12 more eqnarrays in the meantime. The torsion or the contortion field of the E(2) gauge theory is non-trivial even in the case of scalar matter source distribution. Decompose the connection into Levi-Civita one and the contortion part and rewrite the eqnarrays for tetrad field in the formalism of general relativity, then there will appear an effective energy-momentum tensor contributed by the contortion distribution, in addition to the ordinary matter source distribution even for the case of scalar matter source. We expect it to contribute at least part of the dark matter effect. We also examine the holding of the first and second Bianchi identities induced by Jacobi identity of the E(2) gauge theory. The approach of our modified gravity is different from other approach of modified gravity in the sense that we construct the modified gravity by modifying the spacetime symmetry on a large scale and the emergence of effective energy-momentum tensor caused by Lorentz violation effect is due to a purely large scale effect.

Sobre la dinámica de una partícula en rotación usando el concepto de invariancia gauge

<p>Se hace una descripción del movimiento de una partícula en rotación haciendo uso del plano complejo y utilizando procedimientos similares al de la construcción de una teoría gauge local. El análisis permite describir el comportamiento de la partícula partiendo de la exigencia de la invariancia gauge de la ecuación de posición.<br />Invariancia que al ser exigida conduce a la introducción de un parámetro compensatorio que se interpreta como la velocidad angular de la partícula. A partir del análisis se obtienen los efectos dinámicos que determinan su movimiento, los cuales son equivalentes a los obtenidos desde una descripción hecha respecto a un sistema de referencia en rotación haciendo uso de coordenadas polares. Este análisis presenta una manera novedosa de deducir las ecuaciones dinámicas de una partícula en rotación, lo cual representa un aporte original y pedagógico para la enseñanza de la física. © 2016. Acad. Colomb. Cienc. Ex. Fis. Nat.</p>

Composite gauge-bosons made of fermions

We construct a class of Abelian and non-Abelian local gauge theories that consist only of matter fields of fermions. The Lagrangian is compact and local without containing an auxiliary vector field nor a subsidiary condition on the matter fields. Because of the special structure, this Lagrangian can be extended to non-Abelian gauge symmetry only in the case of SU(2) doublet matter fields. We carry out explicit dynamical computation in the leading 1/N order to show that massless spin-one bound states appear with the correct gauge coupling. Our diagram calculation exposes the dynamical features that cannot be explored in the formal auxiliary vector-field trick. For instance, it shows that the s-wave fermion-antifermion interaction alone cannot form the bound gauge-bosons; the fermion-antifermion pairs must couple to the d-wave state too. One feature common to our class of Lagrangian is that the Noether current does not exist. Therefore it evades possible conflict with the no-go theorem of Weinberg and Witten on formation of the non-Abelian gauge bosons.

Análisis de sistemas físicos usando procedimientos análogos a la teoría gauge

en el presente artículo se hace una descripción del movimiento de una partícula en rotación haciendo uso del plano complejo y utilizando procedimientos similares al de la construcción de una teoría gauge local. El análisis permite describir el comportamiento de la partícula partiendo de la exigencia de la invariancia gauge de la ecuación de posición. Invariancia que al ser exigida conduce a la introducción de un parámetro compensatorio que se interpreta como la velocidad angular de la partícula. A partir del análisis se obtienen los efectos dinámicos que determinan su movimiento, los cuales son análogos a los obtenidos desde una descripción hecha respecto a un sistema de referencia en rotación haciendo uso de coordenadas polares. Este tipo de estudio adquiere especial importancia cuando se busca hacer un análisis sobre un sistema en rotación desde una perspectiva diferente a la usualmente establecida.

Solution for a local straight cosmic string in the braneworld gravity

In this work we deal with the spacetime shaped by a straight cosmic string, emerging from local gauge theories, in the braneworld gravity context. We search for physical consequences of string features due to the modified gravitational scenario encoded in the projected gravitational equations. It is shown that cosmic strings in braneworld gravity may present significant differences when compared to the general relativity predictions since its linear density is modified and the deficit angle produced by the cosmic string is attenuated. Furthermore, the existence of cosmic strings in that scenario requires a strong restriction to the braneworld tension: $\lambda \geq 3 \times 10^{-17}$, in Planck units.

What has been discovered at 125 GeV by the CMS and the ATLAS experiments?

While looking for the putative Higgs boson of the Standard Model of particle physics, recently, the CMS and the ATLAS experiments at CERN have found strong signals of a new particle at about 125GeV. However in July 2012 the decay channels of this particle had some unexpected and puzzling anomalies not explainable by the Standard Model. By March 2013 they had seen these signals at about well less than 3\( \sigma\) confidence level. It is expected that the final definitive analysis shall still take quite some time. Here we show that what they may have found at 125GeV is the long sought for and missing ingredient of the strong interaction: the sigma-meson of the Chiral Sigma Model, within the framework of the Skyrme model with a topological interpretation of the baryons. Just like a massless gauge boson is a requirement, and hence a prediction of the local gauge theories, in the the same manner, a very heavy scalar meson is a requirement and hence a prediction of the Skyrme model of the hadrons. The 125GeV particle discovered by the CMS and the ATLAS groups may be an experimental confirmation of this unique prediction of the topological Skyrme model. However the bottom line is that even if the experimentalists finally confirm that this 125GeV entity is the expected Higgs boson, then there still remains to discover another heavier scalar particle as the sigma-meson of the chiral sigma model/Skyrme model, which remains its unique prediction, as shown in this paper.