N=1 formulation of general N=2 Yang-Mills supergravity couplings

We formulate general interactions of an N=2 Yang-Mills supermultiplet coupled to N=2 supergravity in terms of N=1 invariant functions. We show that the N=2 scalar potential of the complex scalar fields in the adjoint representation, superpartners of the Yang-Mills gauge fields, splits into a conventional gauge contribution as well as in a superpotential term contribution proportional to the SO(2) gauge coupling of N=2 de Sitter supergravity. The relation of these results to the σ model structure of N4 extended supergravities is also discussed, particularly in connection with the coset disintegration of scalar manifolds.     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

Gauge fixing, families index theory, and topological features of the space of lattice gauge fields

The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: the topological sectors, specified by the fermionic topological charge, are shown to contain noncontractible even-dimensional spheres when N3, and noncontractible circles in the N=2 case. We describe how certain obstructions to the existence of gauge fixings without the Gribov problem in the continuum setting correspond on the lattice to obstructions to the contractibility of these spheres and circles. We also point out a canonical connection on the space of lattice gauge fields with monopole-like singularities associated with the spheres.     

Geometry of N = 1 dualities in four dimensions

We discuss how N = 1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS branes.     

Instantons and the chiral phase transition

We examine the role of instantons in the zero-temperature chiral phase transition in an SU(N) gauge theory. For a range of N_f (the number of fermion flavors) depending on N, the theory exhibits an infrared fixed point at coupling _*. As N_f decreases, _* increases, and it eventually exceeds a critical value sufficient to trigger chiral symmetry breaking. For the case N = 2, we estimate the critical values of N_f and _* due to instantons by numerically solving a gap equation with an instanton-generated kernel. We find instanton effects of strength comparable to that of gluon exchange.     

Spontaneous localization of bulk fields: the six-dimensional case

We study N=2 supersymmetric gauge theories with d=6 bulk and d=4 brane fields charged under a U(1) gauge symmetry. Radiatively induced Fayet–Iliopoulos terms lead to an instability of the bulk fields. We compute the profile of the bulk zero modes and observe the phenomenon of spontaneous localization towards the position of the branes. While this mechanism is quite similar to the d=5 case, the mass spectrum of the excited Kaluza–Klein modes shows a crucial difference.     

Gauged Goldstone boson effective action from direct integration of bardeen anomaly

We derive the effective action which describes the anomalous Goldstone boson interactions in the presence of external flavour SU(N)_L×SU(N)_R gauge fields, by a direct integration of the Bardeen anomaly. Through comparison with other results, we are able to elucidate the relationship between anomalies based on different regularization schemes. We also give a compact representation of the anomalous part of the fermionic determinant allowing for a simpler rederivation of our results.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

Supermembranes

An example is given of the spontaneous breaking of D = 4, N = 2 global supersymmetry down to N = 1. The example is a four-dimensional membrane in a six-dimensional supersymmetric gauge theory. The effective low-energy action for the membrane is a generalization of the Green—Schwarz covariant action.     

The two-point correlation function of the one-dimensional matrix model

Following Kostov and Ben-Menahem, we calculate the two-puncture correlation function for the one-dimensional matrix model. We find that it depends on the details of discretization for all momenta p. Its only universal features are its vanishing as p → 0 and the appearance of double poles at |p| = n/√′, N = 1,2,…. We show how to derive these double poles in the conformal gauge treatment of Liouville gravity.     

Superconformal invariants and extended supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N = 2 and N = 4 supersymmetric Yang-Mills theory can be evaluated up to constants.     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

由N-E-V分布及赝势法研究弱磁场中弱相互作用费米子气体的热力学性质

基于低温下量子系统的相关实验多是在体积、能量和粒子数都可变的外场束缚下进行的事实, 由体积、能量和粒子数可变的完全开放系统的统计分布(N-E-V分布)研究了弱磁场中弱相互作用费米系统的热力学性质. 首先求出了一般情况下由费米积分表示的内能和热容的解析表达式. 在此基础上, 又给出了在低温极限条件下内能与热容的解析表达式和数值计算结果, 并将N-E-V分布(粒子数密度变化)的结果与赝势法(粒子数密度不变)的结果进行了比较. 结果表明: N-E-V分布方法的计算结果总是补偿赝势法计算结果的过度偏差. 由N-E-V 分布方法所得结果最特异之处在于: 在低温条件下, 弱磁场中弱相互作用费米系统存在一相变温度t_c, 其正处于费米系统发生玻色-爱因斯坦凝聚(BEC)和费米原子形成库珀对的超流状态(BCS)相变及BEC-BCS跨越的温度范围内, 且不随反映弱相互作用大小和特征的散射长度a (a<0引力, a>0斥力)变化, 但随弱磁场的加强而降低, 即弱磁场可调节该相变温度. 磁场为零时, 相变温度最高, 为费米温度的0.184倍.     

Interpolating between Ising, XY-, and non-linear σ-models

The β-functions of O(N)-symmetric non-linear σ-models on the lattice were recently discovered to be non-monotonic for N 3. We explain the non-monotonic behaviour as a non-perturbative lattice effect by relating it to the Kosterlitz-Thouless transition of the XY-model. We also relate the latter transition to the phase transition of the Ising model. These relationships are established by interpolating between the O(N)- and the O(N − 1)-symmetric non-linear σ-models by suppression of the Nth component of the N-vector field with a mass term. A critical line in the coupling-mass plane connects the critical point of the Ising model (N = 1) with the critical point of the XY-model (N = 2). This line extends towards the region of non-monotonic behaviour of the β-function of the O(3)-symmetric model. The nature of the transition lines is also investigated.     

Stabilizing the axion by discrete gauge symmetries

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on Z_N symmetries with N=11,12, etc., are presented realizing the DFSZ axion and the KSVZ axion. The discrete gauge anomalies are canceled by a discrete version of the Green–Schwarz mechanism. In the supersymmetric extension our models provide a natural link between the SUSY breaking scale, the axion scale, and the SUSY-preserving μ term.     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

Constrained effective potential in hot QCD

Constrained effective potentials in hot gauge theory give the probability that a configuration p of the order parameter (Polyakov loop) occurs. They are important in the analysis of surface effects and bubble formation in the plasma. The vector potential appears non-linearly in the loop; in weak coupling the linear term gives rise to the traditional free-energy graphs. But the non-linear terms generate insertions of the constrained modes into the free-energy graphs, through renormalisations of the Polyakov loop. These insertions are gauge dependent and are necessary to cancel the gauge dependence of the free-energy graphs. The latter is shown, through the BRST identities, to have again the form of constrained mode insertions. We stress that the effective action, without this insertion, is gauge variant and gives quite deceptive information. Amongst more it follows, that absolute minima of the potential are at the center group values of the loop, once the insertion is done. We evaluate the two-loop contributions for SU(N) gauge theories, with and without quarks, for the full domain of the N − 1 variables.     

Relativistic field-theoretical equations for the three-body multichannel πN and γN scattering reactions and propagator of the Δ-resonance

A new form of the relativistic three-body equations for the coupled πN and γN scattering reactions with three particle final states ππN and γπN is suggested. These equations are derived in the framework of the time-ordered three dimensional field theory. The solutions of the considered equations satisfy the unitarity condition and are exactly gauge invariant. The form of these three-body equations is does not depend on the choice of the model of Lagrangian and is also the same for the formulations with and without quark degrees of freedom.

The effective potentials of the suggested equations are defined by the vertex functions with two on-mass shell particles. It is emphasized that these input vertex functions can be constructed from experimental data. Special attention is given to the construction of the propagator of the Δ-resonance in the framework of the separable πN potential model. The strong dependence of the multichannel πN and γN cross sections on the form of the Δ-resonance propagator[2] is discussed.

The used formulation of the relativistic three-dimensional and three-body equations allows us to overcome a number of approximations which are usually used by practical calculations of the πN and γN scattering reactions.     

Explicit counteraction algorithms in higher dimensions

Using the background field method we construct algorithms for the one-loop counterterms of a field theory in a space-time of dimension 2, 4, 6, 8 or 10. From the d = 6 algorithm we demonstrate the one-loop finiteness of N = 2 supersymmetric Yang-Mills theories and also N = 1 Yang-Mills theory. All other N = 1 Yang-Mills theories + N = 1 matter theories in d = 6 are shown to have a divergent one-loop S-matrix.

We also present partial results for two- and three-loop algorithms in d = 6 and d = 4 respectively.