We motivate the concept of emergent gauge symmetry and discuss ways that this concept can be tested. The key idea is that if a symmetry is emergent, one should look for small violations of this symmetry because the underlying fundamental theory does not contain the symmetry. We describe our recent work implementing this idea in the gravity sector. We also describe the reasons why violations of gauge symmetry may well be linked to violations of Lorentz invariance.
We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the infrared. Holographic description of the strong coupling is used. The emphasis is made on emergence of chiral fermions in the low-energy theory.
We explore the phenomenon of emergent Lorentz invariance in strongly coupled theories. The strong dynamics is handled using the gauge/gravity correspondence. We analyze how the renormalization group flow towards Lorentz invariance is reflected in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are found to be power-law suppressed by the ratio of the infrared and ultraviolet scales. We show that in a certain subclass of models the velocities of the light bound states st…
We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form o…
Kaluza-Klein gravity is revisted, with renewed interest, in a type IIB string theory on $S^1\times K3$. The irreducible curvature tensors are worked out in the, T-dual, emergent gravity in 4D to yield a non-linear U(1) gauge theory. Interestingly, the T-duality may be seen to describe an open/closed string duality at a self-dual string coupling. The obtained deformation in $AdS_5$ black hole is analyzed to introduce the notion of temperature in the emergent gravity underlying the recent idea of entropic force.
We argue that supersymmetry with its well known advantages, such as naturalness, grand unification and dark matter candidate seems to possess one more attractive feature: it may trigger, through its own spontaneous violation in the visible sector, a dynamical generation of gauge fields as massless Nambu-Goldstone modes during which physical Lorentz invariance itself is ultimately preserved. We consider the supersymmetric QED model extended by an arbitrary polynomial potential of massive vector superfield that breaks gauge invariance in the SUSY invariant phase. However, the requirement of vacu…
Gauge symmetries play an essential role in determining the interactions of particle physics. Where do they come from? Might the gauge symmetries of the Standard Model unify in the ultraviolet or might they be emergent in the infrared, below some large scale close to the Planck scale? Emergent gauge symmetries are important in quantum many-body systems in quantum phases associated with long range entanglement and topological order, e.g., they arise in high temperature superconductors, with string-net condensation and in the A-phase of superfluid He-3. String-nets and superfluid He-3 exhibit eme…
Rigid gauge invariance comprises the symmetry content for physical quantities in a local gauge theory. Its derivation from BRS invariance is thus crucial for determining the physical consequences of the symmetry.
For gauge theory, the matrix element for any physical process is independent of the gauge used. Since this is a formal statement and examples are known where gauge invariance is violated, for any specific process this gauge invariance needs to be checked by explicit calculation. In this paper, gauge invariance is found to hold for a large non-trivial class of processes described by tree diagrams in the standard model -- tree diagrams with two external $W$ bosons and any number of external Higgs bosons. This verification of gauge invariance is quite complicated, and is based on a direct study o…
Hadron properties and interactions are emergent from QCD. Atomic and condensed matter physics are emergent from QED. Could the local gauge symmetries of particle physics also be emergent? We give an introduction to this question and recent ideas connecting it to the (meta)stability of the Standard Model Higgs vacuum. With an emergent Standard Model the gauge symmetries would "dissolve" in the ultraviolet. This scenario differs from unification models which exhibit maximum symmetry in the extreme ultraviolet. With emergence, new global symmetry violations would appear in higher dimensional oper…
A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.
We discuss the Higgs mass and cosmological constant in the context of an emergent Standard Model, where the gauge symmetries "dissolve" in the extreme ultraviolet. In this scenario the cosmological constant scale is suppressed by power of the large scale of emergence and expected to be of similar size to neutrino masses. Cosmology constraints then give an anthropic upper bound on the Higgs mass.
We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct operators which create gauge invariant coloured unparticles. We discuss both their perturbative and non--perturbative properties.
The inconsistence of Dirac-Weyl field equations with the universal U(1) gauge invariance of neutrinos in quantum mechanics led to generalize the special relativity to the generic relativity, which was composed of the special relativity and its three analogues with different signatures of metrics. The combination of the universal U(1) gauge invariance and the generic relativity naturally deduced the strong gauge symmetries $% SU(3)$ and the electroweak ones $SU(2)\times U(1)$ in the Standard Model. The universal U(1) gauge invariance of elementary fermions is attributed to its nature of complex…
First of all, we reconsider the tight - binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D Weitzenbock geometry as well as the emergent U(1) gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+1 D teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations wi…
We study a gauge theory in a 5D warped space via the dimensional deconstruction that a higher dimensional gauge theory is constructed from a moose of 4D gauge groups. By the AdS/CFT correspondence, a 5D warped gauge theory is dual to a 4D conformal field theory (CFT) with a global symmetry. As far as physics of the gauge theory, we obtain the one-to-one correspondence between each component of a moose of gauge groups and that of a CFT. We formulate a supersymmetric extension of deconstruction and explore the framework of natural supersymmetry in a 5D warped space -- the supersymmetric Randall-…
We explore the possibility of gauge mediation in a paradigm whereby supersymmetry is posited to be an accidental symmetry of Nature and the Standard Model fields are composite bound states that emerge from a conformal field theory. The resultant effective theory can, through sequestering and conformal dynamics, exhibit most of the properties of low energy supersymmetry breaking while averting a number of cosmological and astrophysical constraints of the traditional framework of gauge mediation via dynamical supersymmetry breaking. Of particular phenomenological interest is that in our scenario…
Appreciating the classical understanding of the elementary particle the "dynamical" Poincare algebra is developed. It is shown that the "dynamical" Poincare algebra and the equations of motion of particles with arbitrary spin are gauge invariant and that gauge invariance and relativistic invariance stand on equal footings. A "dynamical" non-minimal interaction is constructed explicitly and the Rarita-Schwinger equation is considered in the framework of this "dynamical" interaction.
A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.
Certain (3+1)-dimensional chiral non-Abelian gauge theories have been shown to exhibit a new type of global gauge anomaly, which in the Hamiltonian formulation is due to the fermion zero-modes of a Z-string-like configuration of the gauge potential and the corresponding spectral flow. Here, we clarify the relation between this Z-string global gauge anomaly and other anomalies in both 3+1 and 2+1 dimensions. We then point out a possible trade-off between the (3+1)-dimensional Z-string global gauge anomaly and the violation of CPT and Lorentz invariance.
We describe higher-dimensional theories whose low-energy 4D descriptions contain larger gauge or global symmetry groups. As an example, we construct a Higgsless SU(2) x U(1) model of electroweak symmetry breaking. The 5D SU(2) gauge invariance contains both the weak SU(2) gauge group and a custodial symmetry that protects the rho parameter. Fermions obtain isospin-violating masses while maintaining universal gauge couplings among all three generations. As a further example, we construct a model of chiral color based on a single SU(3).
Gauge invariance and soft limits can be enough to determine the analytic structure of scattering amplitudes in certain theories. This prompts the question of how gauge invariance is connected to analytic structure in more general theories. Here we focus on QED in background plane waves. We show that imposing gauge invariance introduces new virtuality poles into internal momenta on which amplitudes factorise into a series of terms. Each term is gauge invariant, has a different analytic structure in external momenta, and exhibits a hard/soft factorisation. The introduced poles are dictated by in…
We determine the gauge invariance classes of tree level Feynman diagrams in spontaneously broken gauge theories, providing a proof for the formalism of gauge and flavor flips. We find new gauge invariance classes in theories with a nonlinearly realized scalar sector. In unitarity gauge, the same gauge invariance classes correspond to a decomposition of the scattering amplitude into pieces that satisfy the relevant Ward Identities individually. In theories with a linear realized scalar sector in R_ξgauge, no additional nontrivial gauge invariance classes exist compared to the unbroken case.
It is shown that the creation of a monopole is a gauge invariant statement, based on topology. Creating a monopole is independent on the abelian projection in which it is created. This is fundamental in defining an order parameter for detecting dual superconductivity of the QCD vacuum.
We derive a relation between four-fermion QED Green functions of different covariant gauges which defines the gauge dependence completely. We use the derived gauge dependence to check the gauge invariance of atom-like bound state calculations. We find that the existing QED procedure does not provide gauge invariant binding energies. A way to a corrected gauge invariant procedure is pointed out.
The role of gauge invariance in calculating B -> V gamma radiative weak decays is clarified. It is shown that the gauge invariance severely restricts the contributions mediated by the usual weak non-leptonic Hamiltonian dominated by u and c quaks with one photon attachment. Such contributions are found to be almost negligible.
In this PhD-thesis effects from intrinsic transverse momentum are studied in several hard scattering processes with an emphasis on color gauge invariance. The thesis is intended for beginning PhD-students as well as for the experts.
The consistent construction of scattering amplitudes for processes with off-shell initial partons and involving electro-weak interactions is addressed.
Symmetry and quantization are the two major enterprises of theoretical physics; but some argue that quantization can be derived as a necessary condition for symmetry. It is argued here that the Heisenberg uncertainty principle is a necessary condition for gauge invariance in the 5-dimensional Kaluza-Klein theory.
We address emergent higher-form symmetry in Higgs phases with superfluidity. The emergent symmetry appears if a matter field is invariant under a transformation of a common subgroup of gauge and global $\mathrm{U}(1)$ symmetries. We explicitly construct the symmetry generator that is topological and gauge invariant in a low-energy effective theory. Such emergent symmetry is helpful to distinguish the Higgs and other phases with superfluidity, such as phases of QCD at finite density. We also discuss the possibility of phase transition between these phases.
In this paper the problem of the gauge in a bound state calculation is discussed. In particular, in order to verify the gauge invariance in the energy levels expansion, some set of gauge invariant contributions are given.
We investigated the viability of neutralino dark matter in the gauge mediation from emergent supersymmetry proposal. In this proposal, supersymmetry is broken at Planck scale and consequently, the gravitino is superheavy and completely decouples from the low energy theory. Squarks and sleptons obtain their soft masses dominantly through gauge mediation with other mechanisms highly suppressed. The lightest supersymmetric partner, in contrast to traditional gauge mediation, is a neutralino which is also a dark matter candidate. By explicit calculation of the low energy spectra, the parameter spa…
The Helicity Structure Functions in the Drell-Yan process are discussed in a framework of Parton Reggeization Approach, which includes the transverse momentum of initial-state partons in a way compatible with QED gauge-invariance. Relationships with conventional Transverse Momentum Dependent Parton Model formalism are clarified.
We present the first complete calculation performed within the Four Dimensional Regularization scheme (FDR), namely the loop-induced on-shell amplitude for the Higgs boson decay into two photons in an arbitrary R_csi gauge. FDR is a new technique -free of infinities- for addressing multi-loop calculus, which automatically preserves gauge invariance, allowing for a 4-dimensional computation at the same time. We obtained the same result as that assessed in dimensional regularization, thereby explicitly verifying, in a realistic case, that FDR respects gauge invariance.
We show that the naively expected large virtual heavy fermion effects in low energy processes may be screened if the process under consideration contains external gauge bosons constrained by gauge invariance. We illustrate this by a typical example of the process $γγ\to b \bar{b}$. Phenomenological implications are also briefly indicated.
The factorisation of the hard amplitude for exclusive meson production in deep inelastic scattering is considered in the framework of a simple model. It is demonstrated explicitly how gauge invariance ensures the cancellation of non-factorising contributions.
We reconsider monolayer graphene in the presence of elastic deformations. It is described by the tight - binding model with varying hopping parameters. We demonstrate, that the fermionic quasiparticles propagate in the emergent 2D Weitzenbock geometry and in the presence of the emergent U(1) gauge field. Both emergent geometry and the gauge field are defined by the elastic deformation of graphene.
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $α$. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the ope…
The problem of maintaining gauge invariance when truncating the two particle irreducible (2PI) effective action has been studied recently by several authors. Here we give a simple and very general derivation of the gauge dependence identities for the off-shell 2PI effective action. We consider the case where the gauge is fixed by an arbitrary function of the quantum gauge field, subject only to the restriction that the Faddeev-Popov matrix is invertable. We also study the background field gauge. We address the role that these identies play in solving gauge invariance problems associated with p…
Vertex operators for photo- and electro-production of baryon states with arbitrary spin-parity, $ γ+ N\to B(J^P)$, are constructed. The operators obey gauge invariance and analyticity constraints. Analyticity is realized as a requirement of the generalized Siegert theorem for vertex form factors.
We show that the Collins-Soper-Sterman resummation approach to the derivation of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is gauge invariant. The special gauge-dependent parton distribution function employed in the resummation technique is expressed as the convolution of an infrared finite function with the standard distribution function. By means of this convolution relation, we explain how the technique works in summing large logarithmic corrections, and how the gauge invariance of the special distribution function is restored.
The structure of the nonperturbative vector meson vertex function complicates the proof of the factorisation theorem for the reaction $γ^*p\to Vp$. It leads to additional contributions but, in a simple model for the vertex function, gauge invariance ensures that they cancel and factorisation is preserved.
We discuss the problem of gauge invariance of the vector meson photoproduction at small $x$ within the two-gluon exchange model. It is found that the gauge invariance is fulfilled if one includes the graphs with higher Fock states in the meson wave function. Obtained results are used to estimate the amplitudes with longitudinal and transverse photon and vector meson polarization.
It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However, we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy b…
By separating the gluon field into physical and pure-gauge components, the usual Poincaré subalgebra for an interacting system can be reconciled with gauge-invariance when decomposing the total rotation and translation generators of QCD into quark and gluon parts. The gauge-invariant quark/gluon parts act as the generators for the gauge-invariant physical component of the quark/gluon field, not the full quark/gluon field which also contains the gauge degrees of freedom. We clarify that the naive canonical decomposition of generators, while trivially respecting the Poincaré subalgebra, might no…
Institute for Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）
In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.
We argue that through the Wilson lines, gauge invariance has as an effect that the hard functions in weighted spin-asymmetries in hadronic scattering processes are given by gluonic pole cross sections, rather than the usual partonic cross sections.
We derive a generalized Ward identity for color-superconducting quark matter via the functional integral approach. The identity implies the gauge independence of the color-superconducting gap parameter on the quasi-particle mass shell to subleading order in covariant gauge.
In the framework of the soft-collinear effective theory, we present a gauge invariant definition of the transverse momentum broadening probability of a highly-energetic collinear quark in a medium and consequently of the jet quenching parameter $\hat{q}$.
Two models with $SU(3)_C\otimes SU(3)_L\otimes U(1)_N$ gauge symmetry are considered. We show that the masslessness of the photon does not prevent the neutrinos from acquiring Majorana masses. That is, there is no relation between the VEVs of Higgs fields and the electromagnetic gauge invariance contrary to what has been claimed recently.
The application of the background-field method to the electroweak Standard Model is reviewed and further explored. Special emphasis is put on questions of gauge invariance and gauge-parameter (in-)dependence. Owing to the gauge invariance of the background-field effective action, the vertex functions obey simple Ward identities which imply important properties of the vertex functions. Carrying out the renormalization in a way respecting background-field gauge invariance leads to considerable simplifications. The generalization of the background-field method to the non-linear realization of the…
We discuss the gauge invariance of quark-quark potential in QCD in the perturbative treatment, and show that the gauge dependence of the quark-gluon interaction cannot be eliminated. Therefore, the quark-quark potential cannot properly be written in terms of physical variables in the perturbation theory. This is in contrast to the QED case in which the gauge invariance of the electron-photon interaction is guaranteed by the current conservation. As an example, we show that the different choices of the gauge fixing give different Coulomb interactions when the fermion current is not conserved. A…
It is argued that the realization of gauge invariance condition as a consequent of cancellation between the ϕ\toγf0\toγ\pi0\pi0 resonance contribution and a ϕ\toγ\pi0\pi0 background one, suggested in Ref. [1], is misleading.
It is shown how gauge invariance is obtained for the coupling of a photon to a two-body state described by the solution of the Bethe-Salpeter equation. This is illustrated both for a complex scalar field theory and for interaction kernels derived from chiral effective Lagrangians.
An exact expression is derived for the meson production current off the nucleon for real and virtual photons which cleanly separates, in a model-independent manner, a tree-level expression that manifestly preserves local gauge invariance in terms of a generalized Ward-Takahashi identity from transverse final-state-interaction (FSI) terms. As discussed in some detail, this exact formulation is particularly well suited for implementing approximation schemes of exchange-current and FSI contributions (which in practice generally will be necessary) at any level of sophistication without violating l…
