Color structures and permutations

Color structures for tree level scattering amplitudes in gauge theory are studied in order to determine the symmetry properties of the color-ordered sub-amplitudes. We mathematically formulate the space of color structures together with the action of permuting external legs. The character generating functions are presented from the mathematical literature and we determine the decomposition into irreducible representations. Mathematically, free Lie algebras and the Lie operad are central. A study of the implications for sub-amplitudes is initiated and we prove directly that both the Parke-Taylor amplitudes and Cachazo-He-Yuan amplitudes satisfy the Kleiss-Kuijf relations

Few-body calculations of η -nuclear quasibound states

We report on precise hyperspherical-basis calculations of ηNN and ηNNN quasibound states, using energy dependent ηN interaction potentials derived from coupled-channel models of the S11 N⁎(1535) nucleon resonance. The ηN attraction generated in these models is too weak to generate a two-body bound state. No ηNN bound-state solution was found in our calculations in models where ReaηN≲1 fm , with aηN the ηN scattering length, covering thereby the majority of N⁎(1535) resonance models. A near-threshold ηNNN bound-state solution, with η separation energy of less than 1 MeV and width of about 15 MeV, was obtained in the 2005 Green–Wycech model where Re aηN≈1 fm . The role of handling self consistently the subthreshold ηN interaction is carefully studied

Connection between response parameter and anomaly coefficient in two dimensional anomalous fluid

In (1 + 1) dimensional hydrodynamics in presence of the gravitational anomalies, the constitutive relations for the stress tensor contain the response parameters ${{\overline{C}}_1}$ , ${{\overline{C}}_2}$ and the gravitation anomaly coefficients c g , c w . Here it is shown that they are related by the two relations ${{\overline{C}}_1}$ = 4 π 2 c w and ${{\overline{C}}_2}$ = 8π2 c g . This agrees with the earlier findings. I argue that the Israel-Hartle-Hawking vacuum is the natural boundary condition which leads to such relation. Finally, the possible physical implications are discussed

Vacuum condition and the relation between response parameter and anomaly coefficient in (1 + 3) dimensions

The role of Israel-Hartle-Hawking vacuum is discussed for anomalous fluid in presence of both the gauge and gravitational anomalies in (1 + 3) dimensions. I show that imposition of this vacuum condition leads to the relation c ˜ 4 d = − 8 π 2 c m $${\tilde{c}}_{4 d}=-8{\pi}^2{c}_m$$ between the response parameter ( c ˜ 4 d $${\tilde{c}}_{4 d}$$ ) and the anomaly coefficient ( c m ). This establishes a connection between the coefficients appearing in a first order and a third order derivative terms in the constitutive relation

Charge symmetry breaking in Λ hypernuclei revisited

The large charge symmetry breaking (CSB) implied by the Λ binding energy difference ΔBΛ4(0g.s.+)≡BΛ(HeΛ4)−BΛ(HΛ4)=0.35±0.06 MeV of the A=4 mirror hypernuclei ground states, determined from emulsion studies, has defied theoretical attempts to reproduce it in terms of CSB in hyperon masses and in hyperon–nucleon interactions, including one pion exchange arising from Λ– Σ0 mixing. Using a schematic strong-interaction ΛN↔ΣN coupling model developed by Akaishi and collaborators for s -shell Λ hypernuclei, we revisit the evaluation of CSB in the A=4 Λ hypernuclei and extend it to p -shell mirror Λ hypernuclei. The model yields values of ΔBΛ4(0g.s.+)∼0.25 MeV . Smaller size and mostly negative p -shell binding energy differences are calculated for the A=7–10 mirror hypernuclei, in rough agreement with the few available data. CSB is found to reduce by almost 30 keV the 110 keV BΛ10 g.s. doublet splitting anticipated from the hyperon–nucleon strong-interaction spin dependence, thereby explaining the persistent experimental failure to observe the 2exc−→1g.s.− γ -ray transition

A novel solution to the Klein–Gordon equation in the presence of a strong rotating electric field

The Klein–Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the electromagnetic field amplitude. The condition for which the new solution recovers the familiar Volkov wavefunction naturally follows. When not satisfied, significant deviation from the Volkov wavefunction is demonstrated. The new condition is shown to differ by orders of magnitudes from the commonly used one. As this equation describes (neglecting spin effects) the emission processes and the particle motion in Quantum Electrodynamics (QED) cascades, our results suggest that the standard theoretical approach towards this phenomenon should be revised

Improved estimates of the nuclear structure corrections in μ D

We calculate the nuclear structure corrections to the Lamb shift in muonic deuterium by using state-of-the-art nucleon–nucleon potentials derived from chiral effective field theory. Our calculations complement previous theoretical work obtained from phenomenological potentials and the zero range approximation. The study of the chiral convergence order-by-order and the dependence on cutoff variations allows us to improve the estimates on the nuclear structure corrections and the theoretical uncertainty coming from nuclear potentials. This will enter the determination of the nuclear radius from ongoing muonic deuterium experiments at PSI

Stringy horizons

We argue that classical (α ′ ) effects qualitatively modify the structure of Euclidean black hole horizons in string theory. While low energy modes experience the geometry familiar from general relativity, high energy ones see a rather different geometry, in which the Euclidean horizon can be penetrated by an amount that grows with the radial momentum of the probe. We discuss this in the exactly solvable S L 2 ℝ / U 1 $$\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{R}}\right)/\mathrm{U}(1)$$ black hole, where it is a manifestation of the black hole/Sine-Liouville duality

Lessons on black holes from the elliptic genus

We further study the elliptic genus of the cigar SL(2 , ℝ) k / U(1) coset supercon-formal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and non-holomorphic parts that are due to the discrete states and a mismatch in the spectral densities of the continuum, respectively. The mismatch in the continuum is universal, in the sense that it is fully determined by the asymptotic cylindrical topology of the cigar’s throat. Since modularity of the elliptic genus requires both the holomorphic and non-holomorphic parts, the holomorphic term is universal as well. The contribution of the discrete states is thus present even for perturbative strings propagating in the background of large Schwarzschild black holes. We argue that the discrete states live at a stringy distance from the tip of the cigar both from the conformal field theory wave-function analysis and from a holonomy space perspective. Thus, the way string theory takes care of its self-consistency seems to have important consequences for the physics near horizons, even for parametrically large black holes

The black hole interior and a curious sum rule

We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics