Finite temperature behaviour of glueballs in Lattice Gauge Theories

We propose a new method to compute glueball masses in finite temperature Lattice Gauge Theories which at low temperature is fully compatible with the known zero temperature results and as the temperature increases leads to a glueball spectrum which vanishes at the deconfinement transition. We show that this definition is consistent with the Isgur-Paton model and with the expected contribution of the glueball spectrum to various thermodynamic quantities at finite temperature. We test our proposal with a set of high precision numerical simulations in the 3d gauge Ising model and find a good agreement with our predictions.Comment: 4 pages, 4 figure

ξ/ξ2nd\xi/\xi_{2nd} ratio as a tool to refine Effective Polyakov Loop models

Effective Polyakov line actions are a powerful tool to study the finite temperature behaviour of lattice gauge theories. They are much simpler to simulate than the original lattice model and are affected by a milder sign problem, but it is not clear to which extent they really capture the rich spectrum of the original theories. We propose here a simple way to address this issue based on the so called second moment correlation length $\xi_{2nd}$. The ratio $\xi/\xi_{2nd}$ between the exponential correlation length and the second moment one is equal to 1 if only a single mass is present in the spectrum, and it becomes larger and larger as the complexity of the spectrum increases. Since both $\xi$ and $\xi_{2nd}$ are easy to measure on the lattice, this is a cheap and efficient way to keep track of the spectrum of the theory. As an example of the information one can obtain with this tool we study the behaviour of $\xi/\xi_{2nd}$ in the confining phase of the ($D=3+1$) $\mathrm{SU}(2)$ gauge theory and show that it is compatible with 1 near the deconfinement transition, but it increases dramatically as the temperature decreases. We also show that this increase can be well understood in the framework of an effective string description of the Polyakov loop correlator. This non-trivial behaviour should be reproduced by the Polyakov loop effective action; thus, it represents a stringent and challenging test of existing proposals and it may be used to fine-tune the couplings and to identify the range of validity of the approximations involved in their construction.Comment: 1+17 pages, 3 pdf figures; v2: 1+17 pages, 3 pdf figures: discussion in section 1,2 and 5 expanded, misprints corrected; matches journal versio

Width of the flux tube in compact U(1) gauge theory in three dimensions

We study the squared width and the profile of flux tubes in compact U(1) lattice gauge theory in three spacetime dimensions. The results obtained from numerical calculations in the dual formulation of this confining theory are compared with predictions from an effective bosonic-string model and from the dual-superconductor model: it is found that the former fails at describing the quantitative features of the flux tube, while the latter is in good agreement with Monte Carlo data. The analytical interpretation of these results (in the light of the semi-classical analysis by Polyakov) is pointed out, and a comparison with non-Abelian gauge theories in four spacetime dimensions is discussed.Comment: 19 pages, 5 pdf figures; v2: 21 pages, 8 pdf figures: references added, new data and new figures included, discussion slightly revise

Effective String Description of the Confining Flux Tube at Finite Temperature

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio $T_c/\sqrt{\sigma_0}$, the linear increase of the squared width of the flux tube with the interquark distance, or the Temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of and EST approach to confinement.Comment: 40 pages, discussion on the rigid string extended, references added; matches the published versio

Universal power law behaviors in genomic sequences and evolutionary models

We study the length distribution of a particular class of DNA sequences known as 5'UTR exons. These exons belong to the messanger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that both in mouse and in human these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model which may explain this finding. We conjecture that this power law behaviour could indeed be a general feature of higher eukaryotes.Comment: 15 pages, 3 figure

Conformal perturbation of off-critical correlators in the 3D Ising universality class

Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the , $< \epsilon (r) \epsilon (0) >$ and two point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the $s = t r^{\Delta_{t}}$ expansion, where $t$ is the reduced temperature. Our results for $< \sigma (r) \sigma (0) >$ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.Comment: 4 pages, 2 figures, Expanded the discussion of Conformal Perturbation Theor

Comparing the Nambu-Goto string with LGT results

We discuss a way to evaluate the full prediction for the interquark potential which is expected from the effective Nambu-Goto string model. We check the correctness of the prescription reproducing the results obtained with the zeta function regularization for the first two perturbative orders. We compare the predictions with existing Monte Carlo data for the (2+1) dimensional Z(2), SU(2) and SU(3) gauge theories: in the low temperature regime, we find good agreement for large enough interquark distances, but an increasing mismatch between theoretical predictions and numerical results is observed as shorter and shorter distances are investigated. On the contrary, at high temperatures (approaching the deconfinement transition from below) a remarkable agreement between Monte Carlo data and the expectations from the Nambu-Goto effective string is observed for a wide range of interquark distances.Comment: 25 pages, 4 eps figures; added a reference, included remarks, corrected a typo; version accepted for publication in JHE

Self-assembly and DNA binding of the blocking factor in X chromosome inactivation

X chromosome inactivation (XCI) is the phenomenon occurring in female mammals whereby dosage compensation of X-linked genes is obtained by transcriptional silencing of one of their two X chromosomes, randomly chosen during early embryo development. The earliest steps of random X-inactivation, involving counting of the X chromosomes and choice of the active and inactive X, are still not understood. To explain "counting and choice," the longstanding hypothesis is that a molecular complex, a "blocking factor" (BF), exists. The BF is present in a single copy and can randomly bind to just one X per cell which is protected from inactivation, as the second X is inactivated by default. In such a picture, the missing crucial step is to explain how the molecular complex is self-assembled, why only one is formed, and how it binds only one X. We answer these questions within the framework of a schematic Statistical Physics model, investigated by Monte Carlo computer simulations. We show that a single complex is assembled as a result of a thermodynamic process relying on a phase transition occurring in the system which spontaneously breaks the symmetry between the X’s. We discuss, then, the BF interaction with X chromosomes. The thermodynamics of the mechanism that directs the two chromosomes to opposite fates could be, thus, clarified. The insights on the selfassembling and X binding properties of the BF are used to derive a quantitative scenario of biological implications describing current experimental evidences on "counting and choice.