1,100 research outputs found

### Free energy and theta dependence of SU(N) gauge theories

We study the dependence of the free energy on the CP violating angle theta,
in four-dimensional SU(N) gauge theories with N >= 3, and in the large-N limit.
Using the Wilson lattice formulation for numerical simulations, we compute
the first few terms of the expansion of the ground-state energy F(theta) around
theta = 0, F(theta) - F(0) = A_2 theta^2 (1 + b_2 theta^2 + ...). Our results
support Witten's conjecture: F(theta) - F(0) = A theta^2 + O(1/N) for theta <
pi.
We verify that the topological susceptibility has a nonzero large-N limit
chi_infinity = 2A with corrections of O(1/N^2), in substantial agreement with
the Witten-Veneziano formula which relates chi_infinity to the eta' mass.
Furthermore, higher order terms in theta are suppressed; in particular, the
O(theta^4) term b_2 (related to the eta' - eta' elastic scattering amplitude)
turns out to be quite small: b_2 = -0.023(7) for N=3, and its absolute value
decreases with increasing N, consistently with the expectation b_2 = O(1/N^2).Comment: 3 pages, talk presented at the conference Lattice2002(topology). v2:
One reference has been updated, no further change

### The phase structure of the 3-d Thirring model

We study the phase structure of the Thirring model in 3-d and find it to be
compatible with the existence of a non gaussian fixed point of RG. A Finite
Size Scaling argument is included in the equation of state in order to avoid
the assumptions usually needed to extrapolate to the thermodynamical limit.Comment: Talk presented at LATTICE96(other models

### Detecting Dual Superconductivity in the Ground State of Gauge Theory

We explicitly construct a monopole creation operator: its vacuum expectation
value is an order parameter for dual superconductivity, in that, if different
from zero, it signals a spontaneous breaking of the $U(1)$ symmetry
corresponding to monopole charge conservation. This operator is tested by
numerical simulations in compact $U(1)$ gauge theory. Our construction provides
a general recipe for detection of the condensation of any topological soliton.
In particular our operator can be used to detect dual superconductivity of the
QCD vacuum.Comment: 10 pages, 3 figures avalaible on request. REVTE

### Chiral symmetry breaking in the 3-d Thirring model for small $N_f$

We study the dynamical breaking of chiral symmetry in the 3-d Thirring model
for a small number of fermion species. The critical point is identified by
fitting lattice data to an equation of state. The spectrum of the theory is
studied to confirm the phase structure of the model.Comment: 3 pages, 3 figures. Talk presented at Lattice '9

### Topological susceptibility of SU(N) gauge theories at finite temperature

We investigate the large-N behavior of the topological susceptibility in
four-dimensional SU(N) gauge theories at finite temperature, and in particular
across the finite-temperature transition at Tc. For this purpose, we consider
the lattice formulation of the SU(N) gauge theories and perform Monte Carlo
simulations for N=4,6. The results indicate that the topological susceptibility
has a nonvanishing large-N limit for T<Tc, as at T=0, and that the topological
properties remain substantially unchanged in the low-temperature phase. On the
other hand, above the deconfinement phase transition, the topological
susceptibility shows a large suppression. The comparison between the data for
N=4 and N=6 hints at a vanishing large-N limit for T>Tc.Comment: 9 pages, 2 figs, a few discussions added, JHEP in pres

### Vortex solution in 2+1 dimensional Yang-Mills theory at high temperatures

At high temperatures the A_0 component of the Yang--Mills field plays the
role of the Higgs field, and the 1-loop potential V(A_0) plays the role of the
Higgs potential. We find a new stable vortex solution of the
Abrikosov-Nielsen-Olesen type, and discuss its properties and possible
implications.Comment: 8 p., three .eps figures include

### The decay of unstable k-strings in SU(N) gauge theories at zero and finite temperature

Sources in higher representations of SU(N) gauge theory at T=0 couple with
apparently stable strings with tensions depending on the specific
representation rather than on its N-ality. Similarly at the deconfining
temperature these sources carry their own representation-dependent critical
exponents. It is pointed out that in some instances one can evaluate exactly
these exponents by fully exploiting the correspondence between the 2+1
dimensional critical gauge theory and the 2d conformal field theory in the same
universality class. The emerging functional form of the Polyakov-line
correlators suggests a similar form for Wilson loops in higher representations
which helps in understanding the behaviour of unstable strings at T=0. A
generalised Wilson loop in which along part of its trajectory a source is
converted in a gauge invariant way into higher representations with same
N-ality could be used as a tool to estimate the decay scale of the unstable
strings.Comment: 18 pages, 4 figures v2: typos correcte

### Topological susceptibility for the SU(3) Yang--Mills theory

We present the results of a computation of the topological susceptibility in
the SU(3) Yang--Mills theory performed by employing the expression of the
topological charge density operator suggested by Neuberger's fermions. In the
continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 \pm
5 MeV)^4 if F_K is used to set the scale. Our result supports the
Witten--Veneziano explanation for the large mass of the eta'.Comment: Talk presented at Lattice2004(topology); 3 pages, 2 figure

### Renormalization group, trace anomaly and Feynman-Hellmann theorem

We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin to FeynmanâHellmann relations whose derivation for the case at hand is complicated by the construction of the gauge theory Hamiltonian. We bypass this problem by using a renormalisation group equation for composite operators and the trace anomaly. The relations serve as possible definitions of the gluon condensates themselves which are plagued in direct approaches by power divergences. In turn these results might help to determine the contribution of the QCD phase transition to the cosmological constant and test speculative ideas

### The SU(2) Confining Vacuum as a Dual Superconductor

We investigate the dual superconductivity hypothesis in pure SU(2) lattice
gauge theory. We find evidence of the dual Meissner effect both in the
maximally Abelian gauge and without gauge fixing. We also obtain a rather good
extimation of the string tension using the value of the London penetration
length.Comment: 4 pages, uuencoded compressed (using GNU's gzip) tar file containing
1 LaTeX2e file, 5 encapsulated Postscript figures, and espcrc2.sty.
Contribution to Lattice 9

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