Baryons in the effective lagrangian of strongly coupled lattice QCD

The effective action formulation of lattice QCD is extended to incorporate baryons. At strong coupling we find a generalized σ model where the baryons obtain their mass via a non-vanishing vacuum expectation value 〈¯ΦΦ〉. The SU(3) effective potential is worked out for Susskind fermions taking into account the influence of the baryons, and the results are compared with the U(3) theory. The large-N behavior of the SU(N) theory is studied as well. A loop expansion method is proposed for dealing with general multi-component baryon fields in both Susskind's and Wilson's fermion formulations.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Manifest chiral symmetry preservation in the 1N-expanded SU(N) Thirring model

By utilizing manifestly chiral-invariant auxiliary field operators, it is demonstrated that continuous chiral symmetry is preserved explicitly in the $\text{1}\text{N}$ expansion of 2-dimensional theories whose fermions have a Gross-Neveu type of potential. The effective lagrangian derived in the $\text{1}\text{N}$ limit describes a massless scalar field whose derivative coupling to the fermions vanishes as N → ∞, and a decoupled massive scalar field.     

Spectrum of lattice gauge theories with fermions from a 1/d expansion at strong coupling

We study the strong coupling limit of U(N) or SU(N) gauge theories with fermions on a lattice. The integration over the gauge and fermion degrees of freedom is performed by analytic methods, leading to a partition function in terms of localized meson and baryon fields. A method for deriving a systematic expansion in the inverse of the space-time dimension of the corresponding Green functions is developed. It is applied to the study of spontaneous breakdown of chiral symmetry, which occurs for any U(N) or SU(N) theory with fermions in the fundamental representation. Meson and baryon spectra are then computed, and found to be in close agreement with those obtained by numerical methods at finite coupling. The pion decay constant is estimated.     

Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD

A method is proposed for computing effective lagrangians in QCD with N colors using lattice regularization. The meson field lagrangian is worked out in detail in the strong coupling limit with various lattice fermion formulations. For generalized Susskind fermions the spontaneous breakdown U(n) ? U(n) → U(n) (diagonal) is found at large N and a generalized version of the non-linear σ model emerges in a natural way. The Nambu-Goldstone spectrum is investigated and a continuous transition is made to Wilson fermions, for which the effective potential and the ππ scattering amplitude are tested on chiral symmetry. Large d (=dimension) approximations are compared with the large N limit and applied to N = 3.     

Stability of the two-dimensional Fermi polaron

A system composed of an ideal gas of N fermions interacting with an impurity particle in two space dimensions is considered. The interaction between impurity and fermions is given in terms of two-body point interactions whose strength is determined by the two-body binding energy, which is a free parameter of the model. If the mass of the impurity is 1.225 times larger than the mass of a fermion, it is shown that the energy is bounded below uniformly in the number N of fermions. This result improves previous, N-dependent lower bounds, and it complements a recent, similar bound for the Fermi polaron in three space dimensions.     

The Gross-Neveu model at finite temperature at next-to-leading order in the 1/N expansion

We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero temperature. As well known, the discrete chiral symmetry of the (1+1)-dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature T_c; we find that the 1/N approximation breaks down for temperatures below T_c: as the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond T_c, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom.     

Magnetic black holes with string-loop corrections

String-loop corrections to magnetic black holes are studied. 4D effective action is obtained by compactification of the heterotic string theory on the manifold K3×T² or on a suitable orbifold yielding N=1 supersymmetry in 6D. In the resulting 4D theory with N=2 local supersymmetry, the prepotential receives only one-string-loop perturbative correction. The loop-corrected black hole is obtained in two approaches: (i) by solving the system of the Einstein-Maxwell equations of motion derived from the loop-corrected effective action and (ii) by solving the system of spinor Killing equations (conditions for the supersymmetry variations of the fermions to vanish) and Maxwell equations. We consider a particular tree-level solution with the magnetic charges adjusted so that the moduli connected with the metric of the internal two-torus are constant. In this case, the loop correction to the prepotential is independent of coordinates, and it is possible to solve the system of the Einstein-Maxwell and spinor Killing equations in the first order in string coupling analytically. The set of supersymmetric solutions of the loop-corrected spinor Killing equations is contained in a larger set of solutions of the equations of motion derived from the string-loop-corrected effective action. Loop corrections to the metric and dilaton are large at small distances from the center of the black hole.     

Some aspects of a unified approach to gauge,dual and Gribov theories

We consider quantum chromodynamics (QCD) with N_c colours and N_f flavours. Large N expansions for this theory are discussed and their advantages are pointed out, especially in relation to the possibility of unifying gauge, dual and Gribov theories of strong interactions. We first recall how the 1/N_c expansion of 't Hooft can be related to a dual loop expansion with a fixed coupling constant. We point out the necessity for quarkless (purely gluonic) bound states to appear and their importance in maintaining confinement at higher orders in 1/N_c. We show how non-orientable dual loops are reinterpreted in QCD and how a paradox appears when N_f is such that asymptotic freedom is lost. Some recent results of Cornwall and Tiktopoulos are analyzed in leading order in 1/N_c. We then introduce a 1/N expansion at ? ≡ N_f/N_c fixed and show how it is related to the hadronic topological expansion (TE). This allows an unambiguous definition of reggeon field theory concepts such as the bare pomeron and diffractive dissociation in QDC. We are able to relate the parameter ? to the clustering of hadronic final states into resonances. Decreasing ? corresponds to increasing cluster over gap size. Renormalization of the dual coupling constant as a function of ? is discussed and an apparent paradox is resolved. We are also able to shed some new light on the problem of f extinction in the TE.Finally, we compare our approach to other schemes trying to relate different aspects of hadron physics.     

Effective lagrangian of mesons and baryons in the strong-coupling expansion of lattice QCD

U(N) and SU(N) lattice QCD are considered. By using a method of the strong-coupling expansion, the effective lagrangian of hadrons is calculated up to the first order in 1/(g²N). For the Susskind lattice fermions, it is shown that chiral symmetry is spontaneously broken and as a result there appears the Nambu-Goldstone boson (pion). The fermion condensation 〈$\text{ψ}\text{ψ}$t>, the masses of hadrons and the pion decay constant are calculated and compared with the results of Monte Carlo (MC) simulations. In the strong-coupling region, our result of the order parameter 〈$\text{ψ}\text{ψ}$〉 coincides very well with that calculated by MC simulations.     

Ground state of an impurity in a homogeneous system in the hypernetted chain approximation

The hypernetted chain theory of the ground state of a homogeneous N-particle medium NM with an impurity particle is presented. The N identical particles are fermions with spin-isospin degeneracy ν, or bosons (in the limit of ν → ∞). The ground-state wave-function of the system is assumed in the Jastrow form with central, state-independent correlation functions. Central, spin-isospin-dependent two-body interactions both in NM and between the impurity particle and the particles of NM are considered. Expressions for the ground-state energy of the system and for the separation energy of the impurity particle are derived. The simplified case of the chain approximation is also considered.     

Baryons and dual unitarization

Processes involving baryons are discussed in the scheme of dual unitarization. In particular, the topological expansion is generalized to any hadronic S-matrix elements involving baryons and/or mesons. Our expansion is based on a model for the baryon propagator, which is a set of three planar Feynman diagrams joined at a junction line. The resulting expansion is a double expansion in 1/N (N= the number of quark flavours) and in the number of baryon loops. Based on this, several new observations are made in phenomenological problems, and a unifying point of view is stressed. The scheme is evidently crossing invariant, and unitarity constraints are imposed order by order in 1/N and in the baryon loop number.     

Field theory of collective excitations III condensation of four-particle clusters

For many fermions with arbitrary two-body forces we investigate the effective action Г[?, α] where ? is the density matrix including pair correlations and α is the four-particle vertex. The physical state including all radiative corrections is obtained by extremizing Г[?, α] with respect to ? and α. Just as ? ≠ 0 corresponds to non-zero density and condensation of pairs, α ≠ 0 signals the presence of a condensate of four-particle clusters. A simple loop expansion is given for Г[?, α]. To lowest order, the extremum amounts to the Hartree-Fock-Bogoliubov equations. The next two steps bring in the four-particle condensate.     

Stability of the 2 + 2 Fermionic System with Point Interactions

We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m₂ ≈? 0.58 such that the system is stable, i.e., the energy is bounded from below, for \(m \in [m_{2}, m_{2}^{-1}]\). So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system.     

On the validity of the 1N expansion

We consider possible effects that may invalidate the $\text{1}\text{N}$ method in some statistical and field models. Discussion is in the framework of the model of charged, non-relativistic fermions with N-component spin. The static dielectric function ?(q, 0) is predicted to have a pole in N. The real parameter of the $\text{1}\text{N}$ expansion is shown to be an increasing function of the coupling constant.     

On the critical behavior of (2 + 1)-dimensional QED

It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N, where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears forN < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.     

Towards the phase structure of euclidean lattice gauge theories with fermions

We propose the phase structure of abelian and non-abelian lattice gauge theories with fermions. We especially analyse Wilson's lattice action with euclidean discrete space-time. We mainly analyse $\text{〈}\text{ψ}{}_{\mathrm{n}}\text{ψ}{}_{\mathrm{n}}\text{〉}$ as an order parameter for the fermion-gauge coupled system. The Wilson loop integral and plaquette-plaquette two-point function are also useful in working out abelian phase diagrams. We will discuss physical implications of the phase diagrams, especially for the mass spectrum in the lattice continuum limit and chiral symmetry breaking. The 1/N expansion and a random walk idea are used in the formulation and play an important role in computing meson and baryon propagators in the strong coupling limit.     

Yukawa alignment in a multi Higgs doublet model: An effective approach

In the two Higgs doublet model, natural flavour conservation can be achieved through the use of a discrete Z₂$Z_2$ symmetry. A less restrictive condition is the requirement of alignment in the Yukawa sector. So far, alignment has been an ansatz, not rooted in a specific model. In this Letter we present a model for alignment, which starts with 2+N$2+N$ Higgs doublets, with natural flavour conservation imposed by a discrete symmetry. Only two of these scalars couple to the fermions, the other N scalars are in a hidden sector. Assuming that the two scalar doublets coupled to fermions are heavy, their decoupling leads to an effective Yukawa interaction. The latter connects the fermions and the scalars of the hidden sector, and exhibits the same Yukawa coupling matrix for each of the N scalars.     

On dimensional reduction of gauge theories: Symmetric fields and harmonic expansion

We compare the four-dimensional symmetric fields obtained by the coset space dimensional reduction scheme to the infinite tower of fields given by the harmonic expansion in a 4+N dimensional gauge theory coupled to fermions on a space-timeM ⁴ ×S/R.     

Dual resonance theory

It is suggested that a dual model could provide a Born approximation to a complete theory of hadrons. After reviewing various properties of Veneziano model amplitudes, including their underlying algebraic structure, more recent developments are discussed. The spectrum generating algebra is constructed and used to prove the no-ghost theorem for space-time dimension d ? 26. A modification of the Veneziano model incorporating SU(N) symmetry in a dynamical fashion is shown to have critical dimension 26?N. A detailed discussion of the dual pion model and its extension to fermions is presented. It is proved that both the meson and fermion sectors are ghost free for d ? 10. Finally, there is a discussion of nonplanar models and their possible connection with the pomeron singularities arising from nonplanar loop diagrams.