Vacuum energy as a c-function for theories with dynamically generated masses

We argue that in asymptotically free non-Abelian gauge theories possessing the phenomenon of dynamical mass generation the $\beta$ function is negative up to a value of the coupling constant that corresponds to a non-trivial fixed point, in agreement with recent AdS/QCD analysis. This fixed point happens at the minimum of the vacuum energy ($\Omega$), which, as a characteristic of theories with dynamical mass generation, has the properties of a c-function.Comment: 12 pages, 3 figure

On The Phase Transition in D=3 Yang-Mills Chern-Simons Gauge Theory

$SU(N)$ Yang-Mills theory in three dimensions, with a Chern-Simons term of level $k$ (an integer) added, has two dimensionful coupling constants, $g^2 k$ and $g^2 N$; its possible phases depend on the size of $k$ relative to $N$. For $k \gg N$, this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has shown; it can be treated semiclassically. For $k=0$, the theory is badly infrared singular in perturbation theory, a non-perturbative mass and subsequent quantum solitons are generated, and Wilson loops show an area law. We argue that there is a phase transition between these two behaviors at a critical value of $k$, called $k_c$, with $k_c/N \approx 2 \pm .7$. Three lines of evidence are given: First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if $k \leq 29N/12$.The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the $k=0$ case. Second, we study in a rough approximation the free energy and show that for $k \leq k_c$ there is a non-trivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass $M$, while both the condensate and $M$ vanish for $k \geq k_c$. Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass $m$ and a (gauge-invariant) dynamical mass $M$. We show that if M \gsim 0.5 m, there are finite-action quantum sphalerons, while none survive in the classical limit $M=0$, as shown earlier by D'Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as $M \rightarrow 0$.Comment: 36 pages, latex, two .eps and three .ps figures in a gzipped uuencoded fil

Baryonic hybrids: Gluons as beads on strings between quarks

We analyze the ground state of the heavy-quark hybrid system composed of three quarks and a gluon. The known string tension K and approximately-known gluon mass M lead to a precise specification of the long-range non-relativistic part of the potential binding the gluon to the quarks with no undetermined phenomenological parameters, in the limit of large interquark separation R. Our major tool (also used earlier by Simonov) is the use of proper-time methods to describe gluon propagation within the quark system, which reveals the gluon Wilson line as a composite of co-located quark and antiquark lines. We show that (aside from color-Coulomb and similar terms) the gluon potential energy in the presence of quarks is accurately described via attaching these three strings to the gluon, which in equilibrium sits at the middle of the Y-shaped string network joining the three quarks. The gluon undergoes small harmonic fluctuations that slightly stretch these strings and quasi-confine the gluon to the neighborhood of the middle. In the non-relativistic limit (large R) we use the Schrodinger equation, ignoring mixing with l=2 states. Relativistic corrections (smaller R) are applied with a variational principle for the relativistic harmonic oscillator. We also consider the role of color-Coulomb contributions. We find leading non-relativistic large-R terms in the gluon string energy which behave like the square root of K/(MR). The relativistic energy goes like the cube root of K/R. We get an acceptable fit to lattice data with M = 500 MeV. We show that in the quark-antiquark hybrid the gluon is a bead that can slide without friction on a string joining the quark and anti-quark. We comment briefly on the significance of our findings to fluctuations of the minimal surface.Comment: 18 pages, revtex4 plus 8 .eps figures in one .tar.gz fil

Three easy exercises in off-shell string-inspired methods

Off-shell string-inspired methods (OSSIM) calculate off-shell QCD Green's functions using Schwinger-Feynman proper-time techniques, always in the background field method (BFM) Feynman gauge for technical convenience, and so far only at one loop. We already know that these results are gauge-invariant, because this gauge realizes the prescriptions of the Pinch Technique (PT), a Feynman-graph formulation for any gauge, but the idea of the first exercise is to show this directly in OSSIM. In this exercise we extend proper-time OSSIM beyond the BFM Feynman gauge so that one can apply PT algorithms, and show that the intrinsic PT is equivalent to resolving ambiguities in OSSIM in other gauges. In the second exercise we use forty-year-old rules of the author and Tiktopoulos for expressing loop integrals with numerator momenta directly in terms of Feynman parameters after momentum integration (the goal of OSSIM) and show that these rules elegantly and with economy of effort give rise, at least at one loop, to standard OSSIM algorithms. In the third exercise we apply world-line techniques to the problem of the breaking of adjoint strings, requiring a non-perturbative treatment that in the end reduces to a variant of the Schwinger result for production of electron-positron pairs in an electric field. This generalizes OSSIM to non-perturbative processes.Comment: 12 pages, 3 figures, talk given at "From quarks and gluons to hadronic matter: A bridge too far?"[QCD-TNT-III], Trento, Italy, Sept. 2-6, 201