55506208
N-Point Vertex Functions, Ward-Takahashi Identities and Dyson-Schwinger Equations in Thermal QCD/QED in the Real Time Hard-Thermal-Loop Approximation
In this paper we calculate the n-point hard-thermal-loop (HTL) vertex functions in QCD/QED for n= 2, 3 and 4 in the physical representation using the real time formalism (RTF). The result reveals that the n-point HTL vertex functions can be classified into two groups, a) those with odd numbers of external retarded indices, and b) those with even numbers of external retarded indices. The n-point HTL vertex functions with one retarded index, which obviously belong to group a), are identical to the HTL vertex functions that appear in the imaginary time formalism (ITF). All the HTL vertex functions belonging to group a) are O(g 2 T 2 ) and satisfy among them the simple QED-type Ward-Takahashi identities, as in the ITF. Those vertex functions belonging to group b) never appear in the ITF, their existence being characteristic of the RTF, and their HTLs exhibit high temperature behavior that is O(g 2 T 3 ), one power of T higher than usual. Despite this difference, we were able to verify that those HTL vertex functions belonging to group b) also satisfy among themselves the QED-type Ward-Takahashi identities, thus guaranteeing the gauge invariance of the HTLs in the real time thermal QCD/QED. As an application, we explicitly derive the HTL resummed Dyson-Schwinger equations for the physical fermion mass function and for the gauge boson polarization tensor in thermal QCD/QED.
118850311
Phase Structure of Thermal QCD/QED:A Gauge Invariant Solution of the HTL Resummed Improved Ladder Dyson-Schwinger Equation
Based on the hard-thermal-loop resummed improved ladder Dyson-Schwinger quation for the fermion mass function, we propose a procedure how we can get the gauge invariant solution in the sense it satisfies the Ward-Takahashi identity. Results of the numerical analysis are shown and properties of the ``gauge-invariant'' solutions are discussed.
119480216
Chiral Phase Transitions in QED at Finite Temperature Dyson-Schwinger Equation Analysis in the Real Time Hard-Thermal-Loop Approximation
In order to clarify the essential thermal effects that govern the chiral phase transition at finite temperature, we investigate, in the real-time thermal QED, the consequences of the hard-thermal-loop (HTL) resummed Dyson-Schwinger equation for the physical fermion mass function ΣR. Since ΣR is the mass function of an “unstable” quasi-particle in thermal field theories, it necessarily has non-trivial imaginary parts, together with non-trivial wave function renormalization constants. Analyses so far have completely disregarded this fact, despite it being one of the basic outcomes of thermal field theory. The “approximation”, which ignores the imaginary parts of ΣR, gives (non-trivial) constraint equations to be solved simultaneously. For this reason, this approximation cannot be applied consistently except in the trivial case, ΣR = 0. In the present analysis we correctly take this fact into account, and study, in the ladder approximation, the effect of the HTL resummed gauge boson propagator. Our results obtained using numerical analysis, reveal two facts: i) the chiral phase transition is of second order, since the fermion mass is dynamically generated at a critical value of the temperature Tc, or at a critical coupling constant αc, without any discontinuity; and ii) the critical temperature Tc at a fixed value of α is significantly lower than that obtained previously, which means that the restoration of chiral symmetry occurs at a lower temperature than previously expected. The second fact shows the importance of correctly incorporating the essential thermal effect into the analysis of the chiral phase transition. A procedure for taking account of the gauge invariance in the present approximation is also discussed.
15470225
Analysis of the phase structure of thermal QED/QCD through the HTL improved ladder Dyson-Schwinger equation: On the gauge dependence of the solution
We solved with a numerical procedure the HTL improved ladder DS equation for the retarded fermion self-energy function $\Sigma_R$ to study the spontaneous generation of fermion mass in thermal QCD/QED, and studied the gauge-dependence of the solution within a general covariant gauge where the gauge parameter $\xi$ is any constant number. 
With the numerical solutions thus obtained, we found the followings; i) The fermion wave function renormalization function $A(P)$ always deviates largely from unity even at the momentum where the mass is defined, thus the corresponding solutions explicitly contradict with the Ward-Takahashi identity. ii) As a result, the obtained solutions strongly depend on the choice of gauge parameters: the critical temperatures and the critical coupling constants significantly change gauge by gauge. In all gauges we studied in the present analysis, we could not find any solution, having a possibility to be consistent with the Ward-Takahashi identity. Thus we are forced to investigate the procedure to find a gauge which enables us to get a solution being consistent with the Ward-Takahashi identity, otherwise we can not obtain any physically sensible conclusions through the analysis of the point-vertex ladder DS equation no matter how the gauge propagator gets improved.
2677382
Phase Structure of Compact QED from the Sine-Gordon/Massive Thirring Duality
We discuss a phase structure of compact QED in four dimensions by considering the theory as a perturbed topological model. In this scenario we use the singular configuration with an appropriate regularization, and so obtain the results similar to the lattice gauge theory due to the effect of topological objects. In this paper we calculate the thermal pressure of the topological model by the use of a one-dimensional Coulomb gas approximation, which leads to a phase structure of full compact QED. Furthermore the critical-line equation is explicitly evaluated. We also discuss relations between the monopole condensation in compact QED in four dimensions and the chiral symmetry restoration in the massive Thirring model in two dimensions.
27880839
On the classical equivalence of monodromy matrices in squashed sigma model
A bstractWe proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.
119748406
Constraints on the electroweak chiral Lagrangian from the precision data
Abstract In the framework of the effective field theory method, we use the experimental data and the perturbative unitarity bounds to determine the values and uncertainty of all the 11 chiral coefficients ( α i , i = 0 , … , 10 ) of the standard electroweak chiral Lagrangian. Up to linear terms in α i , we provide the one-loop renormalization group equations of all the chiral coefficients, which are calculated in the Feynman–'t Hooft gauge using the modified minimal subtraction scheme. With the improved renormalization group equations to sum over the logarithmic corrections, we analyze the current experimental uncertainty of oblique correction parameters, S ( Λ ) and T ( Λ ) . We find that, due to the large uncertainty in the triple gauge-boson coupling measurements, the parameter space of positive S ( Λ ) for Λ > 1  TeV is still allowed by the current experimental data. T ( Λ ) tends to increase with Λ even in the presence of the operators that contribute to the triple and quartic gauge-boson couplings.
3197539
Type IIA string and matrix string on pp-wave
Abstract We study type IIA string theories on the pp -waves with 24 supercharges. The type IIA pp -wave backgrounds are derived from the maximally supersymmetric pp -wave solution in eleven dimensions through the toroidal compactification on the spatial isometry directions. The associated actions of type IIA strings are obtained by using these metrics and other background fields of the type IIA supergravities on the one hand. On the other hand, we derive these theories from D =11 supermembrane on the pp -wave via double-dimensional reduction for the spatial isometry directions. The resulting actions agree with those of type IIA strings obtained in the study of the supergravities. Also, the action of the matrix string is written down. Moreover, the quantization of closed and open strings is discussed. In particular, we study D p -branes allowed in one of the type IIA theories.
7387924
Deconfining Phase Transition in QCD_4 and QED_4 at Finite Temperature
We investigate the deconfining phase transition in QCD_4 and QED_4 at finite temperature using a perturbative deformation of topological quantum field theory (TQFT). A modified maximal abelian gauge (MAG) is utilized in the analysis. In this case, we can derive the linear potential studying the 2D theory through Parisi-Sourlas (PS) dimensional reduction. The mechanism of deconfining phase transition is proposed. It is geometrical to discuss the thermal effect on the linear potential. All we have to do is to investigate the behavior of topological objects as such instantons and vortices on a cylinder. This is the great advantage of our scenario. This mechanism is also applied in the case of QED_4. The phase structure at the high temperature of QED is investigated using the Coulomb potential on a cylinder. It coincides with the result in the lattice compact U(1) gauge theory. Also, QCD with MAG has the property called the abelian dominance, which enables us to discuss the deconfinement of QCD_4.