Limiting velocities as running parameters and superluminal neutrinos

In the context of theories where particles can have different limiting velocities, we review the running of particle speeds towards a common limiting velocity at low energy. Motivated by the recent OPERA experimental results, we describe a model where the neutrinos would deviate from the common velocity by more than do other particles in the theory, because their running is slower due to weaker interactions.Comment: 5 pages, 3 figure

Noninvertible anomalies in SU(N)×U(1)SU(N)\times U(1) gauge theories

We study $4$-dimensional $SU(N)\times U(1)$ gauge theories with a single massless Dirac fermion in the $2$-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible $0$-form $\widetilde {\mathbb Z}_{2(N\pm 2)}^{\chi}$ chiral symmetry along with a $1$-form $\mathbb Z_N^{(1)}$ center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus $\mathbb T^3$, we construct the non-unitary gauge invariant operator corresponding to $\widetilde {\mathbb Z}_{2(N\pm 2)}^{\chi}$ and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject $\mathbb T^3$ to $\mathbb Z_N^{(1)}$ twists, for $N$ even, in selected magnetic flux sectors, the algebra of $\widetilde {\mathbb Z}_{2(N\pm 2)}^{\chi}$ and $\mathbb Z_N^{(1)}$ fails to commute by a $\mathbb Z_2$ phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the $1$-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary $\mathbb T^3$ size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an Appendix, we also discuss how to construct the corresponding noninvertible defect via the ``half-space gauging'' of a discrete one-form magnetic symmetry.Comment: 22 pages, an Appendix on constructing the noninvertible defect using "half-space gauging'' of a discrete one-form magnetic symmetry is added. References added. Matches the published versio

Design of Fullerene20-thieno[2,3-c]pyrrole-4,6(5H)-dione-fullerene20 for Opto-nonlinear applications: Quantum Mechanical Study

Background: Many organic compounds are studied because of their nonlinear optical properties, which are crucial in photonics, optical switches, modulators, optical data storage, and other devices that use light to transport information. In experimental and theoretical researches, nonlinear optical phenomena, primarily resulting from interactions between matter and strong electric fields, have received considerable attention. Materials like these have numerous applications in science, engineering, and technology. Materials and Methods: Fullerene 20 has been adopted as an electron donor, which was considered an NLO molecular material, while the thieno[2,3-c]pyrrole-4,6(5H)-dione has been adopted as an electron acceptor. Fullerene20-thieno[2,3-c]pyrrole-4,6(5H)-dione-fullerene20 (FTPDF), as D-A-D, has been designed for nonlinear optical applications. Fullerene20-thieno[2,3-c]pyrrole-4,6(5H)-dione-fullerene20 (FTPDF) was studied to determine its linear and nonlinear optical properties. For FTPDF, nonlinear optical properties were calculated with DFT/B3LYP using the basis set 6-31G(d,p). Various quantum calculations determine the structural and symmetry properties of Fullerene20-thieno[2،3-c]pyrrole-4،6(5H)-dione-fullerene20. Results: The rotation increases the electric dipole moment µtot, average linear polarizability αo and the first hyperpolarizability βtot. And the anisotropic polarizability ∆α is smaller than the average polarizability, and the present structure has few deviations from spherical symmetry. FTPDF shows µx-switch behavior. In particular, the rotation can raise the possibility for a new type of molecular βx-switch. Conclusion: The Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) energies estimated by DFT for the investigated molecules have been reported here. Fullerene20-thieno[2,3-c]pyrrole-4,6(5H)-dione-fullerene20 has an increased first hyperpolarizability, making it a novel material suitable for the development of optoelectronic devices

Noninvertible anomalies in SU(N) × U(1) gauge theories

We study 4-dimensional SU(N) × U(1) gauge theories with a single massless Dirac fermion in the 2-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible 0-form Z∼χ2(N±2) chiral symmetry along with a 1-form Z(1)N center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus T 3, we construct the non-unitary gauge invariant operator corresponding to Z∼χ2(N±2) and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject T 3 to Z(1)N twists, for N even, in selected magnetic flux sectors, the algebra of Z∼χ2(N±2) and Z(1)N fails to commute by a ℤ2 phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the 1-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary T 3 size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an appendix, we also discuss how to construct the corresponding noninvertible defect via the “half-space gauging” of a discrete one-form magnetic symmetry

Multi-fractional instantons in SU(N) Yang-Mills theory on the twisted {\mathbbm{T}}^4

We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus T4 with ’t Hooft twisted boundary conditions. These instantons possess topological charge Q=r/N, where 1 ≤ r < N. To implement the twist, we employ SU(N) transition functions that satisfy periodicity conditions up to center elements and are embedded into SU(k) × SU(ℓ) × U(1) ⊂ SU(N), where ℓ + k = N. The self-duality requirement imposes a condition, kL1L2 = rℓL3L4, on the lengths of the periods of T4 and yields solutions with abelian field strengths. However, by introducing a detuning parameter ∆ ≡ (rℓL3L4 – kL1L2)//L1L2L3L4, we generate self-dual nonabelian solutions on a general T4 as an expansion in powers of ∆. We explore the moduli spaces associated with these solutions and find that they exhibit intricate structures. Solutions with topological charges greater than 1/N and k ≠ r possess non-compact moduli spaces, along which the O(^) gauge-invariant densities exhibit runaway behavior. On the other hand, solutions with Q=r/N and k = r have compact moduli spaces, whose coordinates correspond to the allowed holonomies in the SU(r) color space. These solutions can be represented as a sum over r lumps centered around the r distinct holonomies, thus resembling a liquid of instantons. In addition, we show that each lump supports 2 adjoint fermion zero modes

Multi-fractional instantons in SU(N)SU(N) Yang-Mills theory on the twisted T4\mathbb T^4

We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus $\mathbb{T}^4$ with 't Hooft twisted boundary conditions. These instantons possess topological charge $Q=\frac{r}{N}$, where $1\leq r< N$. To implement the twist, we employ $SU(N)$ transition functions that satisfy periodicity conditions up to center elements and are embedded into $SU(k)\times SU(\ell)\times U(1)\subset SU(N)$, where $\ell+k=N$. The self-duality requirement imposes a condition, $k L_1L_2=r\ell L_3L_4$, on the lengths of the periods of $\mathbb{T}^4$ and yields solutions with abelian field strengths. However, by introducing a detuning parameter $\Delta\equiv (r\ell L_3L_4-k L_1 L_2)/\sqrt{L_1 L_2L_3L_4}$, we generate self-dual nonabelian solutions on a general $\mathbb{T}^4$ as an expansion in powers of $\Delta$. We explore the moduli spaces associated with these solutions and find that they exhibit intricate structures. Solutions with topological charges greater than $\frac{1}{N}$ and $k\neq r$ possess non-compact moduli spaces, along which the $O(\Delta)$ gauge-invariant densities exhibit runaway behavior. On the other hand, solutions with $Q=\frac{r}{N}$ and $k=r$ have compact moduli spaces, whose coordinates correspond to the allowed holonomies in the $SU(r)$ color space. These solutions can be represented as a sum over $r$ lumps centered around the $r$ distinct holonomies, thus resembling a liquid of instantons. In addition, we show that each lump supports $2$ adjoint fermion zero modes.Comment: 30 pages+ appendice

Helical Magnetic Fields from Inflation

We analyze the generation of seed magnetic fields during de Sitter inflation considering a non-invariant conformal term in the electromagnetic Lagrangian of the form $-\frac14 I(\phi) F_{\mu \nu} \widetilde{F}^{\mu \nu}$, where $I(\phi)$ is a pseudoscalar function of a non-trivial background field $\phi$. In particular, we consider a toy model, that could be realized owing to the coupling between the photon and either a (tachyonic) massive pseudoscalar field and a massless pseudoscalar field non-minimally coupled to gravity, where $I$ follows a simple power-law behavior $I(k,\eta) = g/(-k\eta)^{\beta}$ during inflation, while it is negligibly small subsequently. Here, $g$ is a positive dimensionless constant, $k$ the wavenumber, $\eta$ the conformal time, and $\beta$ a real positive number. We find that only when $\beta = 1$ and $0.1 \lesssim g \lesssim 2$ astrophysically interesting fields can be produced as excitation of the vacuum, and that they are maximally helical.Comment: 17 pages, 1 figure, subsection IIc and references added; accepted for publication in IJMP