Light-like noncommutativity,light-front quantization and new light on UV/IR mixing

We revisit the problem of quantizing field theories on noncommutative Moyal space–time with light-like   noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p⁺$p^{+}$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.     

The gauging of BV algebras

A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending on the nature of the global symmetry, the gauging involves coupling to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling to an N=0$N=0$ ghost system yields an ordinary gauge theory whose observables are appropriately classified by the invariant BV cohomology. Coupling to an N=1$N=1$ ghost system leads to a topological gauge field theory whose observables are classified by the equivariant BV cohomology. Coupling to higher N$N$ ghost systems yields topological gauge field theories with higher topological symmetry. In the latter case, however, problems of a completely new kind emerge, which call for a revision of the standard BV algebraic framework.     

String modular phases in Calabi–Yau families

We investigate the structure of singular Calabi–Yau varieties in moduli spaces that contain a Brieskorn–Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the L$L$-series for singular fibers for several families. We find that the resulting motivic L$L$-functions agree with the L$L$-series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic L$L$-functions are identical in several cases to L$L$-series derived from weighted Fermat hypersurfaces. This shows that singular Calabi–Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi–Yau varieties of different dimensions.     

Global supersymmetry on curved spaces in various dimensions

We propose methods towards a systematic determination of d  -dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids Hⁿ⁺¹${\mathbb{H}}^{n+1}$ and compact spheres Sⁿ${\mathbb{S}}^n$ or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on S¹×Sⁿ${\mathbb{S}}^1\times {\mathbb{S}}^n$, with n<6$n<6$. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres S^d${\mathbb{S}}^d$ if d>5$d>5$ (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification.     

Entanglement entropy of round spheres

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a (d−2)$(d-2)$-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near horizon geometry of the latter is H₂×S_d−2$H_2\times S_{d-2}$. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the “brick wall” model of 't Hooft. The case of generic 4d conformal field theory is discussed.     

Some remarks on defects and T-duality

The equations of motion for a conformal field theory in the presence of defect lines can be derived from an action that includes contributions from bibranes. For T-dual toroidal compactifications, they imply a direct relation between Poincaré line bundles and the action of T-duality on boundary conditions. We also exhibit a class of diagonal defects that induce a shift of the B-field. We finally study T-dualities for S¹$S^1$-fibrations in the example of the Wess–Zumino–Witten model on SU(2)$\mathrm{SU}(2)$ and lens spaces. Using standard techniques from D-branes, we derive from algebraic data in rational conformal field theories geometric structures familiar from Fourier–Mukai transformations.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

Spin vortices in the Abelian–Higgs model with cholesteric vacuum structure

We continue the study of U(1)$U\left(1\right)$ vortices with cholesteric vacuum structure. A new class of solutions is found which represent global vortices of the internal spin field. These spin vortices are characterized by a non-vanishing angular dependence at spatial infinity, or winding. We show that despite the topological Z₂${\mathbb{Z}}_2$ behavior of SO(3)$SO\left(3\right)$ windings, the topological charge of the spin vortices is of the Z$\mathbb{Z}$ type in the cholesteric. We find these solutions numerically and discuss the properties derived from their low energy effective field theory in 1+1$1+1$ dimensions.     

Varying vacuum energy of a self-interacting scalar field

Understanding mechanisms capable of altering the vacuum energy is currently of interest in field theories and cosmology. We consider an interacting scalar field and show that the vacuum energy naturally takes any value between its maximum and zero because interaction affects the number of operating field modes, the assertion that involves no assumptions or postulates. The mechanism is similar to the recently discussed temperature evolution of collective modes in liquids. The cosmological implication concerns the evolution of scalar field ?$?$ during the inflation of the Universe. ?$?$ starts with all field modes operating and maximal vacuum energy in the early inflation-dominated epoch. As a result of inflation, ?$?$ undergoes a dynamical crossover and arrives in the state with one long-wavelength longitudinal mode and small positive vacuum energy predicted to be asymptotically decreasing to zero in the late epoch. Accordingly, we predict that the currently observed cosmological constant will decrease in the future, and comment on the possibility of a cyclic Universe.     

Absence of tricritical behavior of the random field Ising model in a honyecomb lattice

In this letter, we study the behavior of the random field Ising model on a honeycomb lattice by means of the effective field theory. We obtain the phase diagram in the T$T$–H$H$ plane for clusters with one spin in a finite size cluster scheme and it is observed the absence of a tricritical point.     

Adiabatic Landau–Zener transitions at avoided level crossings with fast noise

Effects of a fast classical noise on adiabatic   Landau–Zener (LZ) transitions between the (2S+1)$(2S+1)$ Zeeman multiplets (diabatic states) of an arbitrary spin S$S$ at an avoided level crossing are investigated. The spin system is simultaneously coupled to a slow regular magnetic field and a fast   random field with Gaussian realizations. In the longitudinal direction, the magnetic field changes its sign at the degeneracy point (and is unbounded at large positive and negative times t=±∞$t=\pm \infty$ far from the degeneracy point) while in its single transverse direction, it remains of constant amplitude. The noise is considered in the limit where its characteristic correlation time (decay time) is small enough compared to the characteristic time of adiabatic LZ transitions. With these considerations, the condition for adiabatic evolution allows us to analytically evaluate the populations of diabatic levels and coherence factors. The study is first implemented for two- (S=1/2$S=1/2$) and three- (S=1$S=1$) state systems and finally extended to arbitrary S$S$. A numerical study is implemented allowing us to check/confirm the range of validity of our analytical solutions. We found a satisfactory quantitative agreement between numerical and analytical data.     

A six-dimensional gauge-Higgs unification model based on E6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E₆ on S²/Z₂$S^2/Z_2$ orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S²$S^2$ and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.     

Affine group formulation of the Standard Model coupled to gravity

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ$\Lambda$, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of the Chern–Simons functional Q$Q$, forms the affine commutation relation with the volume element V(x)$V\left(x\right)$. Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant.     

On the geometry of prequantization spaces

Given a Poisson (or more generally Dirac) manifold P$P$, there are two approaches to its geometric quantization: one involves a circle bundle Q$Q$ over P$P$ endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P$P$. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P$P$ is obtained from the Lie groupoid of Q$Q$ via an S¹$S^1$ reduction that preserves both the Lie groupoid and the geometric structures.     

Theory of twist liquids: Gauging an anyonic symmetry

Topological phases in (2+1)$(2+1)$-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids  , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z₂${\mathbb{Z}}_2$-symmetric toric code, SO(2N)₁$SO{\left(2N\right)}_1$ and SU(3)₁$SU{\left(3\right)}_1$ state as well as the S₃$S_3$-symmetric SO(8)₁$SO{\left(8\right)}_1$ state and a non-Abelian chiral state we call the “4-Potts” state.     

Classical and quantum theory of the massive spin-two field

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz–Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark–antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers J^PC=2⁻⁺$J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.