Symmetric Theory Research Articles

String diagram rewrite theory III: Confluence with and without Frobenius

AbstractIn this paper, we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorially as double-pushout rewriting with interfaces (DPOI) on (labelled) hypergraphs. For standard DPO rewriting without interfaces, confluence for terminating rewriting systems is, in general, undecidable. Nevertheless, we show here that confluence for DPOI, and hence string diagram rewriting, is decidable. We apply this result to give effective procedures for deciding local confluence of symmetric monoidal theories with and without Frobenius structure by critical pair analysis. For the latter, we introduce the new notion of path joinability for critical pairs, which enables finitely many joins of a critical pair to be lifted to an arbitrary context in spite of the strong non-local constraints placed on rewriting in a generic symmetric monoidal theory.

Nonmetricity theories and aspects of gauge symmetry

In this paper we discuss on the phenomenological viability of nonmetricity theories of gravity which are based in the class of generalized Weyl spacetimes---denoted by ${W}_{4}$---where arbitrary nonmetricity is allowed. This class of geometry includes the so called teleparallel spaces ${Z}_{4}$, which are the geometric bases of the symmetric teleparallel theories. The guiding principle in our discussion is Weyl gauge symmetry, which is a manifest symmetry of ${W}_{4}$ spaces. Here we derive the master equation that drives the gauge-invariant variations of the length of vectors during parallel transport in ${W}_{4}$. This is the mathematical basis of the second clock effect (SCE). We are able to give qualitative and quantitative estimates for the SCE, as well as for the perihelion shift, in the coincident gauge of ${Z}_{4}$ space. We conclude that generalized Weyl spaces do not represent phenomenologically viable descriptions of nature due to the SCE and, also to their predictions for the perihelion shift. All of the present results are based on the assumption of: (i) a gauge invariant parallel transport law, and (ii) a consistency hypothesis which enables identifying hypothetical vectors and tensors defined in ${W}_{4}$, with related physical vectors and tensors arising in the given gravitational theory. Our discussion is mostly geometrical without relying on specific theories of gravity, unless it is absolutely necessary.

Effective field theories for gapless phases with fractons via a coset construction

Fractons are particles with restricted mobility. We give a symmetry-based derivation of effective field theories of gapless phases with fractonic topological defects, such as solids and supersolids, using a coset construction. The resulting theory is identified as the Cosserat elasticity theory, which reproduces the conventional symmetric elasticity theory at low energies. The construction can be viewed as a dynamical realization of the inverse Higgs mechanism. We incorporate topological defects such as dislocations and disclinations, which are nontrivially related by the Bianchi identities of defect gauge fields. The origin of the fractonic nature of defects in those systems can be traced back to the semidirect product structure of translational and rotational groups. The construction is immediately extendable to higher dimensions and systems with broken translational symmetries, such as solids, supersolids, and vortex crystals. We identify Wess-Zumino terms in supersolids, which induce quasiparticle scatterings on topological defects.

Parity from gauge symmetry

We argue that Left-Right parity symmetry {mathcal {P}} can arise as a discrete remnant of a unified gauge symmetry. The high-energy unification necessarily includes the gauging of the Lorentz symmetry, bringing into the game gravitational interactions, and leading to a gravi-GUT scheme. Parity emerges unbroken below the Planck scale, and can be broken spontaneously at lower energies making contact with the Standard Model. This framework motivates the spontaneous origin of parity violation as in Left-Right symmetric theories with {mathcal {P}}. The possible unifying gauge groups are identified as mathrm{SO}(1,7) for gravitational and weak interactions, or mathrm{SO}(7,7) for a complete unification.

Fractons in curved space

We consistently couple simple continuum field theories with fracton excitations to curved spacetime backgrounds. We consider homogeneous and isotropic fracton field theories, with a conserved U(1) charge and dipole moment. Coupling to background fields allows us to consistently define a stress-energy tensor for these theories and obtain the respective Ward identities. Along the way, we find evidence for a mixed gauge-gravitational anomaly in the symmetric tensor gauge theory which naturally couples to conserved dipoles. Our results generalise to systems with arbitrarily higher conserved moments, in particular, a conserved quadrupole moment.

Symmetries of conformal correlation functions

A program of wide interest in modern conformal bootstrap studies is to numerically solve general conformal field theories, based on a critical assumption that the dynamics is encoded in the conformal four-point crossing equations and positivity condition. In this paper we propose and verify a novel algebraic property of the crossing equations which provides strong restriction for this program. We show for various types of symmetries $\mathcal{G}$, the crossing equations can be linearly converted into the $SO(N)$ vector crossing equations associated with the $SO(N)\ensuremath{\rightarrow}\mathcal{G}$ branching rules and the transformations satisfy positivity condition. The dynamics constrained by the $\mathcal{G}$-symmetric crossing equations combined with the positivity condition degenerates to the $SO(N)$ symmetric cases, while the non-$SO(N)$ symmetric theories are not directly solvable without introducing the $SO(N)$ symmetry breaking assumptions on the spectrum.

Schur apolarity

Inspired by the classic apolarity theory of symmetric tensors, the aim of this paper is to introduce the Schur apolarity theory, i.e. an apolarity for any irreducible representation of the special linear group SL(V). This allows to describe decompositions of structured tensors whose elementary elements are tensors that represent flags of the vector space V. The main result is the Schur apolarity lemma which is the analogous of the apolarity lemma of symmetric apolarity theory. Eventually we study the rank tensors of low border rank related to specific varieties giving rise also to simple algorithms.

Neutrino: Chronicles of an aloof protagonist

In this paper, we give a brief account of the history of neutrino, and how that most aloof of all particles shaped our search for a theory of fundamental interactions ever since it was theoretically proposed. We introduce the necessary concepts and phenomena in a nontechnical language aimed at a physicist with some basic knowledge of quantum mechanics. In showing that neutrino mass could be the door to new physics beyond the Standard Model, we emphasize the need to frame the issue in the context of a complete theory, with testable predictions accessible to present and near future experiments. We argue in favor of the minimal Left–Right symmetric theory as the strongest candidate for such theory, connecting neutrino mass with parity breakdown in nature. This is the theory that led originally to neutrino mass and the seesaw mechanism behind its smallness, but even more important, the theory that sheds light on a fundamental question that touches us all: the symmetry between left and right.

Search for Majorana neutrinos exploiting millikelvin cryogenics with CUORE

The possibility that neutrinos may be their own antiparticles, unique among the known fundamental particles, arises from the symmetric theory of fermions proposed by Ettore Majorana in 19371. Given the profound consequences of such Majorana neutrinos, among which is a potential explanation for the matter–antimatter asymmetry of the universe via leptogenesis2, the Majorana nature of neutrinos commands intense experimental scrutiny globally; one of the primary experimental probes is neutrinoless double beta (0νββ) decay. Here we show results from the search for 0νββ decay of 130Te, using the latest advanced cryogenic calorimeters with the CUORE experiment3. CUORE, operating just 10 millikelvin above absolute zero, has pushed the state of the art on three frontiers: the sheer mass held at such ultralow temperatures, operational longevity, and the low levels of ionizing radiation emanating from the cryogenic infrastructure. We find no evidence for 0νββ decay and set a lower bound of the process half-life as 2.2 × 1025 years at a 90 per cent credibility interval. We discuss potential applications of the advances made with CUORE to other fields such as direct dark matter, neutrino and nuclear physics searches and large-scale quantum computing, which can benefit from sustained operation of large payloads in a low-radioactivity, ultralow-temperature cryogenic environment.

Calculating critical temperature and critical exponents by self-similar approximants

Abstract Self-similar approximation theory allows for defining effective sums of asymptotic series. The method of self-similar factor approximants is applied for calculating the critical temperature and critical exponents of the O(N)-symmetric φ 4 field theory in three dimensions by summing asymptotic ε expansions. This method is shown to be essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons U(1)×U(1) Abelian Higgs model

While the phase structure of the $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$-symmetric Higgs theory is still under debate, a version of this theory with an additional Chern-Simons term was recently shown to undergo a second-order phase transition [Vira Shyta et al., Phys. Rev. Lett. 127, 045701 (2021)]. This theory is dual to a topological field theory of massless fermions featuring two gauge fields. Here we elaborate on several aspects of this duality, focusing on the critical current correlators and on the nature of the critical point as reflected by the bosonization duality. The current correlators associated with the $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry and the topological current are shown to coincide up to a universal prefactor, which we find to be the same for both $U(1)$ and $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$ topological Higgs theories. The established duality offers in addition another way to substantiate the claim about the existence of a critical point in the bosonic Chern-Simons $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$ Higgs model: a Schwinger-Dyson analysis of the fermionic dual model shows that no dynamical mass generation occurs. The same cannot be said for the theory without the Chern-Simons term in the action.

Modular symmetry in the SMEFT

We study the modular symmetric standard model effective field theory. We employ the stringy Ansatz on coupling structure that 4-point couplings ${y}^{(4)}$ of matter fields are written by a product of 3-point couplings ${y}^{(3)}$ of matter fields, i.e., ${y}^{(4)}={y}^{(3)}{y}^{(3)}$. In this framework, we discuss the flavor structure of bilinear fermion operators and 4-fermion operators, where the holomorphic and antiholomorphic modular forms appear. From the Ansatz, the ${A}_{4}$ modular-invariant semileptonic four-fermion operator $[{\overline{E}}_{R}\mathrm{\ensuremath{\Gamma}}{E}_{R}][{\overline{D}}_{R}\mathrm{\ensuremath{\Gamma}}{D}_{R}]$ does not lead to the flavor changing (FC) processes since this operator would be constructed in terms of gauge couplings $g$ as ${y}^{(3)}\ensuremath{\sim}g$. The chirality flipped bilinear operator $[{\overline{D}}_{R}\mathrm{\ensuremath{\Gamma}}{D}_{L}]$ also does not lead FC if the mediated mode corresponds to the Higgs boson ${H}_{d}$. In this case, the flavor structure of this operator is the exactly same as the mass matrix. On the other hand, if the flavor structure of the operator is not the exactly same as the mass matrix, the situation would change drastically. Then, we obtain the nontrivial relations of FC transitions at nearby fixed points $\ensuremath{\tau}=i,\ensuremath{\omega},i\ensuremath{\infty}$, which are testable in the future. As an application, we discuss the relations of the lepton flavor violation processes $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma},\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ at nearby ${\ensuremath{\tau}}_{e}=i$, where the successful lepton mass matrix was obtained. We also study the flavor changing 4-quark operators in the ${A}_{4}$ modular symmetry of quarks. As a result, the minimal flavor violation could be realized by taking relevant specific parameter sets of order one.

Spacetime symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

We explore if space-time symmetric lattice field theory models with a finite Hilbert space per lattice site can reproduce asymptotic freedom in the two-dimensional $O(4)$ model. We focus on a simple class of such models with a five dimensional local Hilbert space. We demonstrate how even the simplest model reproduces asymptotic freedom within the D-theory formalism but at the cost of increasing the size of the Hilbert space through coupling several layers of a two-dimensional lattice. We then argue that qubit regularization can be viewed as an effective field theory (EFT) even if the continuum limit cannot be reached, as long as we can tune the model close enough to the continuum limit where perturbation theory, or other analytical techniques, become viable. We construct a simple lattice model on a single layer with a four dimensional local Hilbert space that acts like an excellent EFT of the original theory.

Efficient simulation of the dynamics of an n -dimensional PT -symmetric system with a local-operations-and-classical-communication protocol based on an embedding scheme

$\mathcal{PT}$-symmetric quantum theory has attracted extensive attention in recent years because of its novel properties, applications, and even controversial discussions. Many difficulties in applications stem from the unknown of how to simulate the dynamics of $\mathcal{PT}$-symmetric systems in conventional quantum systems. In this work, by clarifying some common confusion in the simulation of $\mathcal{PT}$-symmetric systems, we are able to naturally extend the application scope of the original embedding simulation scheme from pure states to arbitrary mixed states. Based on the above groundwork, we further propose a local-operations-and-classical-communication (LOCC) protocol scheme to simulate the dynamics of a $\mathcal{PT}$-symmetric system. Our LOCC protocol scheme, which needs one ancillary qubit only, can be applied to simulate any arbitrary finite-dimensional $\mathcal{PT}$-symmetric system in the $\mathcal{PT}$-unbroken phase and has several advantages over the original embedding scheme. The success probability is increased to ${\ensuremath{\lambda}}_{min}$ (${\ensuremath{\lambda}}_{min}>1$) times in general, even approaching $100%$ in some special cases, and has a concise bound that makes it easier to estimate the necessary experimental resources in advance. Furthermore, our LOCC protocol has less dependence on but more flexibility in the selection of the metric operator and more adaptability in practical applications, and it is more consistent with the physical intuition. Finally, the physical or philosophical meaning behind the embedding scheme and the LOCC protocol is discussed.

Rip cosmological models in extended symmetric teleparallel gravity

In this paper we have investigated some rip cosmological models in an extended symmetric teleparallel gravity theory. We consider the form $f(Q,T)=aQ^m+bT$ in the Einstein-Hilbert action and expressed the field equations and the dynamical parameters in terms of the non-metricity $Q$. Three rip models such as Little Rip, Big Rip and Pseudo Rip are presented. The energy conditions and the cosmographic parameters are derived and analysed for all these models.

Critical Field Theories with OSp(1|2M) Symmetry

In the paper [L. Fei etal., J. High Energy Phys. 09 (2015) 076JHEPFG1029-847910.1007/JHEP09(2015)076] a cubic field theory of a scalar field σ and two anticommuting scalar fields, θ and θ[over ¯], was formulated. In 6-ε dimensions it has a weakly coupled fixed point with imaginary cubic couplings where the symmetry is enhanced to the supergroup OSp(1|2). This theory may be viewed as a "UV completion" in 2<d<6 of the nonlinear sigma model with hyperbolic target space H^{0|2} described by a pair of intrinsic anticommuting coordinates. It also describes the q→0 limit of the critical q-state Potts model, which is equivalent to the statistical mechanics of spanning forests on a graph. In this Letter we generalize these results to a class of OSp(1|2M) symmetric field theories whose upper critical dimensions are d_{c}(M)=2[(2M+1)/(2M-1)]. They contain 2M anticommuting scalar fields, θ^{i}, θ[over ¯]^{i}, and one commuting one, with interaction g(σ^{2}+2θ^{i}θ[over ¯]^{i})^{(2M+1)/2}. Ind_{c}(M)-ε dimensions, we find a weakly coupled IR fixed point at an imaginary value of g. We propose that these critical theories are the UV completions of the sigma models with fermionic hyperbolic target spaces H^{0|2M}. Of particular interest is the quintic field theory with OSp(1|4) symmetry, whose upper critical dimension is 10/3. Using this theory, we make a prediction for the critical behavior of the OSp(1|4) lattice system in three dimensions.

A renormalizable left-right symmetric model with low scale seesaw mechanisms

We propose a low scale renormalizable left-right symmetric theory that successfully explains the observed SM fermion mass hierarchy, the tiny values for the light active neutrino masses and is consistent with the lepton and baryon asymmetries of the Universe, the muon and electron anomalous magnetic moments as well as with the constraints arising from the meson oscillations. In the proposed model the top and exotic quarks obtain masses at tree level, whereas the masses of the bottom, charm and strange quarks, tau and muon leptons are generated from a tree level Universal Seesaw mechanism, thanks to their mixings with the charged exotic vector like fermions. The masses for the first generation SM charged fermions arise from a radiative seesaw mechanism at one loop level, mediated by charged vector like fermions and electrically neutral scalars. The light active neutrino masses are produced from a one-loop level inverse seesaw mechanism mediated by electrically neutral scalar singlets and right handed Majorana neutrinos. Our model is also consistent with the experimental constraints arising from the Higgs diphoton decay rate as well as with the constraints arising from charged lepton flavor violation. We also discuss the Z′ and heavy scalar production at a proton-proton collider.

Monodromy defects from hyperbolic space

We study monodromy defects in O(N) symmetric scalar field theories in d dimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory on S1 × Hd−1, where Hd−1 is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition along S1. In this description, the codimension two defect lies at the boundary of Hd−1. We first study the general monodromy defect in the free field theory, and then develop the large N expansion of the defect in the interacting theory, focusing for simplicity on the case of N complex fields with a one-parameter monodromy condition. We also use the ϵ-expansion in d = 4 − ϵ, providing a check on the large N approach. When the defect has spherical geometry, its expectation value is a meaningful quantity, and it may be obtained by computing the free energy of the twisted theory on S1 × Hd−1. It was conjectured that the logarithm of the defect expectation value, suitably multiplied by a dimension dependent sine factor, should decrease under a defect RG flow. We check this conjecture in our examples, both in the free and interacting case, by considering a defect RG flow that corresponds to imposing alternate boundary conditions on one of the low-lying Kaluza-Klein modes on Hd−1. We also show that, adapting standard techniques from the AdS/CFT literature, the S1 × Hd−1 setup is well suited to the calculation of the defect CFT data, and we discuss various examples, including one-point functions of bulk operators, scaling dimensions of defect operators, and four-point functions of operator insertions on the defect.

Scale and conformal invariance in higher derivative shift symmetric theories

The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta function depends non trivially only on the anomalous dimension. The trace of the energy momentum tensor is also investigated and it is shown that these two families of QFTs are conformally invariant at the fixed point of the RG flow.

Planar black holes configurations and shear viscosity in arbitrary dimensions with shift and reflection symmetric scalar-tensor theories

In higher dimensions, we explore planar hairy black hole configurations for a special subclass of the Horndeski theory defined by two coupling functions depending on the kinetic term and enjoying shift symmetry and reflection symmetry. For this analysis, we derive a set of new solutions given by time-dependent as well as time-independent scalar field configurations. Additionally, we calculate their thermodynamic quantities by using Wald formalism satisfying the first law of thermodynamics as well as a Smarr relation. Together with the above, the Wald procedure allows us to compute the shear viscosity, showing that for a suitable choice of the coupling functions the Kovtun-Son-Starinets bound is violated.