Dirac and non-Dirac conditions in the 2-potential theory of magnetic charge

We investigate the Cabbibo-Ferrari, two potential approach to magnetic charge coupled to two different complex scalar fields, $\Phi_1$ and $\Phi_2$, each having different electric and magnetic charges. The scalar field, $\Phi_1$, is assumed to have a spontaneous symmetry breaking self interaction potential which gives a mass to the "magnetic" gauge potential and "magnetic" photon, while the other "electric" gauge potential and "electric" photon remain massless. The magnetic photon is hidden until one reaches energies of the order of the magnetic photon rest mass. The second scalar field, $\Phi _2$, is required in order to make the theory non-trivial. With only one field one can always use a duality rotation to rotate away either the electric or magnetic charge, and thus decouple either the associated electric or magnetic photon. In analyzing this system of two scalar fields in the Cabbibo-Ferrari approach we perform several duality and gauge transformations, which require introducing non-Dirac conditions on the initial electric and magnetic charges. We also find that due to the symmetry breaking the usual Dirac condition is altered to include the mass of the magnetic photon. We discuss the implications of these various conditions on the charges.Comment: revtex 9 pages, 1 figure, to be published EPJ

A line of CFTs: from generalized free fields to SYK

We point out that there is a simple variant of the SYK model, which we call cSYK, that is $SL(2,R)$ invariant for all values of the coupling. The modification consists of replacing the UV part of the SYK action with a quadratic bilocal term. The corresponding bulk dual is a non-gravitational theory in a rigid AdS$_2$ background. At weak coupling cSYK is a generalized free field theory; at strong coupling, it approaches the infrared of SYK. The existence of this line of fixed points explains the previously found connection between the three-point function of bilinears in these two theories at large $q$.Comment: 26 pages, v

The Bulk Dual of SYK: Cubic Couplings

The SYK model, a quantum mechanical model of $N \gg 1$ Majorana fermions $\chi_i$, with a $q$-body, random interaction, is a novel realization of holography. It is known that the AdS$_2$ dual contains a tower of massive particles, yet there is at present no proposal for the bulk theory. As SYK is solvable in the $1/N$ expansion, one can systematically derive the bulk. We initiate such a program, by analyzing the fermion two, four and six-point functions, from which we extract the tower of singlet, large $N$ dominant, operators, their dimensions, and their three-point correlation functions. These determine the masses of the bulk fields and their cubic couplings. We present these couplings, analyze their structure and discuss the simplifications that arise for large $q$.Comment: 39 pages, v2: Evaluation of integral in Sec. 3.3.2 correcte

All point correlation functions in SYK

Large $N$ melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together. We uncover an incredibly useful property of these theories: the six-point function, or equivalently, the three-point function of the primary $O(N)$ invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions, to leading nontrivial order in $1/N$, through simple Feynman-like rules. The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point functions. We explicitly calculate the bilinear three-point function for $q$-body SYK, at any $q$. This leads to the bilinear four-point function, as well as all higher-point functions, expressed in terms of higher-point conformal blocks, which we discuss. We find universality of correlators of operators of large dimension, which we simplify through a saddle point analysis. We comment on the implications for the AdS dual of SYK.Comment: 67 pages, v

The Evolution of Multicomponent Systems at High Pressures: VI. The Thermodynamic Stability of the Hydrogen-Carbon System: The Genesis of Hydrocarbons and the Origin of Petroleum

The spontaneous genesis of hydrocarbons which comprise natural petroleum have been analyzed by chemical thermodynamic stability theory. The constraints imposed upon chemical evolution by the second law of thermodynamics are briefly reviewed; and the effective prohibition of transformation, in the regime of temperatures and pressures characteristic of the near-surface crust of the Earth, of biological molecules into hydrocarbon molecules heavier than methane is recognized. A general, first-principles equation of state has been developed by extending scaled particle theory (SPT) and by using the technique of the factored partition function of the Simplified Perturbed Hard Chain Theory (SPHCT). The chemical potentials, and the respective thermodynamic Affinity, have been calculated for typical components of the hydrogen-carbon (H-C) system over a range pressures between 1-100 kbar, and at temperatures consistent with those of the depths of the Earth at such pressures. The theoretical analyses establish that the normal alkanes, the homologous hydrocarbon group of lowest chemical potential, evolve only at pressures greater than approximately thirty kbar, excepting only the lightest, methane. The pressure of thirty kbar corresponds to depths of approximately 100 km. Special high-pressure apparatus has been designed which permits investigations at pressures to 50 kbar and temperatures to 2000 K, and which also allows rapid cooling while maintaining high pressures. The high-pressure genesis of petroleum hydrocarbons has been demonstrated using only the solid reagents iron oxide, FeO, and marble, CaCO3, 99.9% pure and wet with triple-distilled water

Geodesic equivalence and integrability

We suggest a construction that, given a trajectorial diffeomorphism between two Hamiltonian systems, produces integrals of them. As the main example we treat geodesic equivalence of metrics. We show that the existence of a non-trivially geodesically equivalent metric leads to Liouville integrability, and present explicit formulae for integrals.Comment: 19 pages; LaTe

Relativistic corrections of m\alpha^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions

The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\infty\alpha^4. In this work we complete calculations of various contributions to the R_\infty\alpha^4 order by computing the relativistic corrections to the binding energy of electron.Comment: 4 pages, 1 figur