Effective Gauge Theory Research Articles

γ5algebra ambiguities in Feynman amplitudes: Momentum routing invariance and anomalies inD=4andD=2

We address the subject of chiral anomalies in two and four dimensional theories. Ambiguities associated with the $\gamma_5$ algebra within divergent integrals are identified, even though the physical dimension is not altered in the process of regularization. We present a minimal prescription that leads to unique results and apply it to a series of examples. For the particular case of abelian theories with effective chiral vertices, we show: 1- Its implication on the way to display the anomalies democratically in the Ward identities. 2- The possibility to fix an arbitrary surface term in such a way that a momentum routing independent result emerges. This leads to a reinterpretation of the role of momentum routing in the process of choosing the Ward identity to be satisfied in an anomalous process. 3- Momentum Routing Invariance (MRI) is a necessary and sufficient condition to assure vectorial gauge invariance of effective chiral Abelian gauge theories. We also briefly discuss the case of complete chiral theories, using the Chiral Schwinger Model as an example.

Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

We propose a $\mathbb{U}(1) \times \mathbb{Z}_2$ effective gauge theory for vortices in a $p_x+ip_y$ superfluid in two dimensions. The combined gauge transformation binds $\mathbb{U}(1)$ and $\mathbb{Z}_2$ defects so that the total transformation remains single-valued and manifestly preserves the the particle-hole symmetry of the action. The $\mathbb{Z}_2$ gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the $\mathbb{U}(1)$ gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. More importantly, it predicts a universal Abelian phase, $\exp(i\pi/8)$, upon the exchange of two vortices. This phase is modified by non-universal corrections due to the partial Chern-Simon term, which are nevertheless screened in a charged superfluid at distances that are larger than the penetration depth.

A surprising relation for the effective coupling constants of N = 2 super Yang-Mills theories

We show that the effective coupling constants $\tau$ of supersymmetric gauge theories described by hyperelliptic curves do not distinguish between the lattices of the two kinds of heterotic string. In particular, the following relation $$ \Theta_{D_{16}^+}(\tau)=\Theta_{E_8}^2(\tau) $$ holds. This is reminiscent of the relation, by $T$-duality, of the two heterotic strings. We suggest that such a relation extends to all curves describing effective supersymmetric gauge theories.

Fractional topological insulators: From sliding Luttinger liquids to Chern-Simons theory

The sliding Luttinger liquids (LL) approach is applied to study fractional topological insulators (FTI). We show that FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interaction. We find that the topological phase pertains in the presence of interaction that breaks the spin invariance and its boundaries are even extended by those terms. Finally we show that one dimensional chiral anomaly in the LL leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state.

Renormalization group equations and matching in a general quantum field theory with kinetic mixing

We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework.

Matrix theory origins of non-geometric fluxes

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and non-associative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of non-associativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.

Models of three-dimensional fractional topological insulators

Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle $\ensuremath{\theta}$ of 0 or $\ensuremath{\pi}$. It was recently shown that fractional quantized values of $\ensuremath{\theta}$ are consistent with time-reversal invariance if deconfined, gapped, fractionally charged bulk excitations appear in the low-energy spectrum due to strong correlation effects, leading to the concept of a fractional topological insulator. These fractionally charged excitations are coupled to emergent gauge fields, which ensure that the microscopic degrees of freedom, the original electrons, are gauge-invariant objects. A first step towards the construction of microscopic models of fractional topological insulators is to understand the nature of these emergent gauge theories and their corresponding phases. In this work, we show that low-energy effective gauge theories of both Abelian or non-Abelian type are consistent with a fractional quantized axion angle if they admit a Coulomb phase or a Higgs phase with gauge group broken down to a discrete subgroup. The Coulomb phases support gapless but electrically neutral bulk excitations while the Higgs phases are fully gapped. The Higgs and non-Abelian Coulomb phases exhibit multiple ground states on boundaryless spatial three-manifolds with nontrivial first homology, while the Abelian Coulomb phase has a unique ground state. The ground-state degeneracy receives an additional contribution on manifolds with boundary due to the induced boundary Chern-Simons term.

Charge and spin fractionalization in strongly correlated topological insulators

We construct an effective topological Landau–Ginzburg theory that describes general SU(2) incompressible quantum liquids of strongly correlated particles in two spatial dimensions. This theory characterizes the fractionalization of quasiparticle quantum numbers and statistics in relation to the topological ground-state symmetries, and generalizes the Chern–Simons, BF (‘background field’) and hierarchical effective gauge theories to an arbitrary representation of the SU(2) symmetry group. We mainly focus on fractional topological insulators with time-reversal symmetry, which are treated as SU(2) generalizations of the quantum Hall effect.

Baryonic popcorn

In the large N limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices expand into the transverse dimension, eventually becoming a higher dimensional (4D) multi-layer lattice at large densities. We consider 3D lattices of zero size instantons as well as 1D periodic chains of finite size instantons, which serve as toy models of the full holographic systems. In particular, for the finite-size case we determine solutions of the corresponding ADHM equations for both a straight chain and for a 2D zigzag configuration where instantons pop up into the holographic dimension. At low density the system takes the form of an "abelian anti-ferromagnetic" straight periodic chain. Above a critical density there is a second order phase transition into a zigzag structure. An even higher density yields a rich phase space characterized by the formation of multi-layer zigzag structures. The finite size of the lattices in the transverse dimension is a signal of an emerging Fermi sea of quarks. We thus propose that the popcorn transitions indicate the onset of the "quarkyonic" phase of the cold dense nuclear matter.

From fixed points to the fifth dimension

Four-dimensional Lorentzian conformal field theory (CFT) is mapped onto 5D anti-de Sitter spacetime (AdS) from the viewpoint of ``geometrizing'' conformal current algebra. A large-$N$ expansion of the CFT is shown to lead to (infinitely many) weakly coupled AdS particles, in one-to-one correspondence with minimal color-singlet CFT primary operators. If all but a finite number of ``protected'' primary operators have very large scaling dimensions, it is shown that there exists a low AdS curvature effective field theory regime for the corresponding finite set of AdS particles. Effective 5D gauge theory and general relativity on AdS are derived in this way from the most robust examples of protected CFT primaries, Noether currents of global symmetries and the energy-momentum tensor. Witten's prescription for computing CFT local-operator correlators within the AdS dual is derived. The main new contribution is the derivation of 5D locality of AdS couplings. This is accomplished by studying a confining IR deformation of the CFT in the large-$N$ ``planar'' approximation, where the discrete spectrum and existence of an $S$ matrix allow the constraints of unitarity and crossing symmetry to be solved (in standard fashion) by a tree-level expansion in terms of 4D local ``glueball'' couplings. When the deformation is carefully removed, this 4D locality (with plausible assumptions specifying its precise nature) combines with the restored conformal symmetry to yield 5D AdS locality. The sense in which AdS/CFT duality illustrates the possibility of emergent relativity and the special role of strong coupling are briefly discussed. Care is taken to conclude each step with well-defined mathematical expressions and convergent integrals.

Universal Monopole Scaling near Transitions from the Coulomb Phase

Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge theory becomes confining, provide examples of unconventional criticality. This Letter studies the behavior at nonzero monopole density near such transitions, using scaling theory to arrive at universal expressions for the crossover phenomena. For a particular transition in spin ice, quantitative predictions are made by mapping to the XY model and confirmed using Monte Carlo simulations.

BPS dyons and Hesse flow

We revisit BPS solutions to classical N=2 low energy effective gauge theories. It is shown that the BPS equations can be solved in full generality by the introduction of a Hesse potential, a symplectic analog of the holomorphic prepotential. We explain how for non-spherically symmetric, non-mutually local solutions, the notion of attractor flow generalizes to gradient flow with respect to the Hesse potential. Furthermore we show that in general there is a non-trivial magnetic complement to this flow equation that is sourced by the momentum current in the solution.

Soft Collinear Degeneracies in an Asymptotically Free Theory

In asymptotically free theories with collinear divergences it is sometimes claimed that these divergences are cancelled if one sums over initial and final state degenerate cross-sections and uses an off-shell renormalisation scheme. We show for scalarϕ3theory in six dimensions that there are further classes of soft collinear divergences and that they are not cancelled. Furthermore, they yield a nonconvergent series of terms at a fixed order of perturbation theory. Similar effects in gauge theories are also summarised.

One-loop adjoint masses for non-supersymmetric intersecting branes

We consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative corrections for the adjoint scalars on the brane world-volumes. In the open string channel, the string two-point function receives contributions only from the infrared and the ultraviolet limits. The latter is due to tree-level closed string uncanceled NS-NS tadpoles, which we explicitly reproduce from the effective Born-Infeld action. On the other hand, the infrared region reproduces the one-loop mediation of supersymmetry breaking in the effective gauge theory, via messengers and their Kaluza-Klein excitations. In the toroidal set-up considered here, it receives contributions only from N ≈ 4 and N ≈ 2 supersymmetric configurations, and thus always leads at leading order to a tachyonic direction, in agreement with effective field theory expectations.

One-Dimensional Chern-Simons Theory

We study a one-dimensional toy version of the Chern-Simons theory. We construct its simplicial version which comprises features of a low-energy effective gauge theory and of a topological quantum field theory in the sense of Atiyah.

SU(3)L ⋊ (ℤ3 × ℤ3) GAUGE SYMMETRY AND TRI-BIMAXIMAL MIXING

We study an effective gauge theory whose gauge group is a semidirect product G = G c ⋊ Γ with G c and Γ being a connected Lie group and a finite group, respectively. The semidirect product is defined through a projective homomorphism (i.e. homomorphism up to the center of G c ) from Γ into G c . To be specific, we take SU (3) L as G c and ℤ3 × ℤ3 as Γ. We notice that the irreducible representations of the gauge group G necessarily contain three G c -multiplets in spite of the Abelian nature of Γ = ℤ3 × ℤ3. This triplication phenomenon is due to the semidirect product structure of G. We suggest that the appearance of three families is attributable to this triplication. We give a toy model on the lepton mixing and show that under a particular vacuum alignment the tri-bimaximal mixing matrix is reproduced.

Remarks on quiver gauge theories from open topological string theory

We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.

A NOTE ON MATRIX MODEL WITH IR CUTOFF AND AdS/CFT

We study effective gauge theory at finite temperature on a three-sphere in the presence of an IR cutoff using AdS/CFT. Comparing with the thermodynamic behavior of its gravity dual, we analyze a phenomenological matrix model which describes the gauge theory in the strongly coupled regime. Subsequently, we study the behavior of the model as a function of the IR cutoff. We further argue that a similar matrix model represents the effective gauge theory on R3 with an IR-cutoff and analyze the model numerically.

Electromagnetic response and pseudo-zero-mode Landau levels of bilayer graphene in a magnetic field

The electromagnetic response of bilayer graphene in a magnetic field is studied in comparison to that of monolayer graphene. Both types of graphene turn out to be qualitatively quite similar in dielectric and screening characteristics, especially those deriving from vacuum fluctuations, but the effect is generally much more sizable for bilayers. The presence of the zero-(energy-)mode Landau levels is a feature specific to graphene. In bilayers, unlike in monolayers, the effect of the zero-mode levels becomes visible and even dominant in density response as an externally controllable band gap develops. It is pointed out that the splitting of nearly degenerate pseudo-zero-mode levels at each valley, which are specific to bilayer graphene, is controlled by an applied inplane electric field or by an injected current. In addition, a low-energy effective gauge theory of bilayer graphene is constructed.

Deconfined quantum criticality driven by Dirac fermions in SU(2) antiferromagnets

Quantum electrodynamics in $2+1$ dimensions is an effective gauge theory for the so-called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul et al., Nat. Phys. 4, 28 (2008)]. In this context, by using the renormalization group in $d=4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions, we show that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species ${N}_{f}\ensuremath{\ge}4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of ${N}_{f}$. In particular, for ${N}_{f}=4$ and $\ensuremath{\epsilon}=1$ $(d=2+1)$, the anomalous dimension of the N\'eel field is given by ${\ensuremath{\eta}}_{N}=1/3$, with a correlation length exponent $\ensuremath{\nu}=1/2$. These values considerably change for ${N}_{f}>4$. For instance, for ${N}_{f}=6$, we find ${\ensuremath{\eta}}_{N}\ensuremath{\approx}0.75\text{ }191$ and $\ensuremath{\nu}\ensuremath{\approx}0.660\text{ }09$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, ${G}_{\ensuremath{\chi}}(x)\ensuremath{\equiv}⟨\overline{\ensuremath{\psi}}(x)\ensuremath{\psi}(x)\overline{\ensuremath{\psi}}(0)\ensuremath{\psi}(0)⟩$.