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Register a new userOn the existence of the global conformal gauge in string theory
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M. O. Katanaev
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The global conformal gauge is playing the crucial role in string theory providing the basis for quantization. Its existence for two-dimensional Lorentzian metric is known locally for a long time. We prove that if a Lorentzian metric is given on a plain then the conformal gauge exists globally on the whole ${mathbb R}^2$. Moreover, we prove the existence of the conformal gauge globally on the whole worldsheets represented by infinite strips with straight boundaries for open and closed bosonic strings. The global existence of the conformal gauge on the whole plane is also proved for the positive definite Riemannian metric.
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In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along certain direction - the so called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function $chi({bf r})$ which rotates the string to another one has quite complicated behaviors depending on which side from which the position variable ${bf r}$ gets across the plane expanded by the two strings. Consequently, some misunderstandings in the literature are clarified.
We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions, on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using a new method local analysis, we conjecture that the conformal region exists together with the confining region and the deconfining region in the phase structure parametrized by beta and K, both in the cases of the large Nf QCD within the conformal window (referred as Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the chiral transition temperature (referred as High Temperature QCD). Our numerical simulation on a lattice of the size 16^3 x 64 shows the following evidence of the conjecture. In the conformal region we find the vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative effects and temporal propagators of meson behave at large t as a power-law corrected Yukawa-type decaying form. The transition from the conformal region to the deconfining region or the confining region is a sharp transition between different vacua and therefore it suggests a first order transition both in Conformal QCD and in High Temperature QCD. Within our fixed lattice simulation, we find that there is a precise correspondence between Conformal QCD and High Temperature QCD in the temporal propagators under the change of the parameters Nf and T/Tc respectively. In particular, we find the correspondence between Conformal QCD with Nf = 7 and High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson unparticle model. From this we estimate the anomalous mass dimension gamma* = 1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc --> infty is a free quark state in the Z(3) twisted vacuum.
It was recently pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.
We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of Morita equivalences, as suggested by higher gauge theory. The zero locus of our moment map is given by the solutions of the Calabi system, a coupled system of equations which provides a unifying framework for the classical Calabi problem and the Hull-Strominger system. Our main results are concerned with the geometry of the moduli space of solutions, and assume a technical condition which is fulfilled in examples. We prove that the moduli space carries a pseudo-Kahler metric with Kahler potential given by the dilaton functional, a topological formula for the metric, and an infinitesimal Donaldson-Uhlenbeck-Yau type theorem. Finally, we relate our topological formula to a physical prediction for the gravitino mass in order to obtain a new conjectural obstruction for the Hull-Strominger system.
In this paper, $E_6$ and especially $E_7$ GUT are considered in the F-theory setting in view of the free fermionic construction of the $4D$ heterotic string. In particular, the NAHE-Based LRS model of cite{Cleaver:2000ds, Cleaver:2002ps} is revisited as an illustration where the starting point was taken to be the $N=4$, $E_7 times E_7 times SO(16)$ which through the use of boundary condition basis vectors is reduced to obtain the flipped $SO(10)$ GUT symmetry. We also seek to extend the results of cite{Faraggi:2002ah} in the case of the flipped $SU(5)$ to home in on the flipped $SO(10)$ vacua from the Horv{a}va-Witten theory where the $E_8$ gauge group on the observable sector decomposes as $E_{8}supset E_{6}times SU(3)$ with $E_{6}$ being the gauge group of the effective field theory. We find for the $E_{6}$ GUT symmetry, solutions of type A and solutions of type B where the Hirzebruch surfaces are considered for the base contrary to cite{Faraggi:2002ah} where flipped $SU(5)$ vacua were studied and only solutions of type B were found. Moreover, no solutions are found in the case of the base being the del Pezzo surfaces. Furthermore, this goes hand in hand with the heterotic, low-energy string-derived effective model discussed in cite{Ashfaque:2016psv,Ashfaque:2016ydg}.
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