No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

Supersymmetry relics in one-flavor QCD from a new 1/N expansion

We suggest a new large-N(c) limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N(c)) QCD keeping quarks in the latter. We can then define a new 1/N(c) expansion (at a fixed number of flavors N(f)) that shares appealing properties with the topological (fixed N(f)/N(c)) expansion while being more suitable for theoretical analysis. In particular, for N(f)=1, our large-N(c) limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for N(f)=1 massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.     

Anomalous superfluidity in (2+1)-dimensional two-color lattice QCD

We study thermodynamics of strongly coupled lattice QCD with two colors of staggered fermions in 2+1 dimensions. The partition function of this model can be written elegantly as a statistical mechanics of dimers and baryon loops. The model is invariant under an SO(3) x U(1) symmetry. At low temperatures, we find evidence for superfluidity in the U(1) symmetry sector while the SO(3) symmetry remains unbroken. The finite temperature phase transition appears to belong to the Kosterlitz-Thouless universality class, but the superfluid density jump rho(s) (T(c)) at the critical temperature T(c) is anomalously higher than the normal value of 2T(c)/pi. We show that, by adding a small SO(3) symmetry breaking term to the model, the superfluid density jump returns to its normal value, implying that the extra symmetry causes anomalous superfluid behavior. Our results may be of interest to researchers studying superfluidity in spin-1 systems.     

Nonperturbative dynamics of noncommutative gauge theory

We present a nonperturbative lattice formulation of noncommutative Yang–Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with p·n_f flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n_f species of matter on a lattice of size p·L with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.     

QCD at finite isospin density

QCD at finite isospin chemical potential mu(I) has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu(I), where chiral perturbation theory is applicable, and at asymptotically high mu(I), where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.     

Membranes on an orbifold

We provide an M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infrared moduli space of SO(4) and SO(5) super Yang-Mills theory, respectively. For higher Chern-Simons level, the moduli space is a quotient of M. At a generic point in the moduli space, the massive spectrum is proportional to the area of the triangle formed by the two membranes and the orbifold fixed point.     

Failure of mean field theory at large N

We study strongly coupled lattice QCD with N colors of staggered fermions in 3+1 dimensions. While mean field theory describes the low temperature behavior of this theory at large N, it fails in the scaling region close to the finite temperature second order chiral phase transition. The universal critical region close to the phase transition belongs to the 3D XY universality class even when N becomes large. This is in contrast to Gross-Neveu models where the critical region shrinks as N (the number of flavors) increases and mean field theory is expected to describe the phase transition exactly in the limit of infinite N. Our work demonstrates that infrared fluctuations can be important close to second order phase transitions even when N is strictly infinite.     

Bs and Ds decay constants in three-flavor lattice QCD

Capitalizing on recent advances in lattice QCD, we present a calculation of the leptonic decay constants f(B(s)) and f(D(s)) that includes effects of one strange sea quark and two light sea quarks via an improved staggered action. By shedding the quenched approximation and the associated lattice scale uncertainty, lattice QCD greatly increases its predictive power. Nonrelativistic QCD is used to simulate heavy quarks with masses between 1.5m(c) and m(b). We arrive at the following results: f(B(s))=260+/-7+/-26+/-8+/-5 and f(D(s))=290+/-20+/-29+/-29+/-6 MeV. The first quoted error is the statistical uncertainty, and the rest estimate the sizes of higher order terms neglected in this calculation. All of these uncertainties are systematically improvable by including another order in the weak coupling expansion, the nonrelativistic expansion, or the Symanzik improvement program.     

QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.     

Electromagnetic nucleon-to-delta transition in chiral effective-field theory

We perform a relativistic chiral effective-field theory calculation of pion electroproduction off the nucleon (e- N --> e- N(pi)) in the delta(1232)-resonance region. After fixing the three low-energy constants, corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) gammaNdelta couplings, our calculation provides a prediction for the momentum transfer and pion-mass dependence of the gammaNdelta form factors. The prediction for the pion-mass dependence resolves the discrepancy between the recent lattice QCD results and the experimental value for the "C2/M1 ratio" at low Q2.     

Accurate determinations of alpha(s) from realistic lattice QCD

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to (1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations), (2) include third-order terms in perturbation theory, (3) systematically estimate fourth and higher-order terms, (4) use an unambiguous lattice spacing, and (5) use an [symbol: see text](a2)-accurate QCD action. We use 28 different (but related) short-distance quantities to obtain alpha((5)/(MS))(M(Z)) = 0.1170(12).     

Explosive percolation is continuous, but with unusual finite size behavior

We study four Achlioptas-type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entirely holomorphic. The distributions of the order parameter, i.e., the relative size s(max)/N of the largest cluster, are double humped. But-in contrast to first-order phase transitions-the distance between the two peaks decreases with system size N as N(-η) with η>0. We find different positive values of β (defined via (s(max)/N)～(p-p(c))β for infinite systems) for each model, showing that they are all in different universality classes. In contrast, the exponent Θ (defined such that observables are homogeneous functions of (p-p(c))N(Θ)) is close to-or even equal to-1/2 for all models.     

Precision model independent determination of |Vub| from B --> pilnu

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented. At large q(2) the form factor is taken from unquenched lattice QCD, at q(2) = 0 we impose a model independent constraint obtained from B --> pipi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |V(ub)| = (3.54 +/- 0.170 +/- 0.44) x 10(-3). With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.     

Quantum Orbifolds

This is a study of orbifold-quotients of quantum groups (quantum orbifolds \({\Theta } \rightrightarrows G_{q}\)). These structures have been studied extensively in the case of the quantum S U ₂ group. A generalized theory of quantum orbifolds over compact simple and simply connected quantum groups is developed. Associated with a quantum orbifold there is an invariant subalgebra and a crossed product algebra. For each spin quantum orbifold, there is a unitary equivalence class of Dirac spectral triples over the invariant subalgebra, and for each effective spin quantum orbifold associated with a finite group action, there is a unitary equivalence class of Dirac spectral triples over the crossed product algebra. A Hopf-equivariant Fredholm index problem is studied as an application.     

Lattice QCD with chemical potential: Evading the fermion-sign problem

Since the turn of the millennium there has been tremendous progress in understanding QCD at finite chemical potential, μ. Apart from qualitative results obtained using models, and exact results at very large μ obtained in weak coupling theory, there has been tremendous progress in getting exact and quantitative results from lattice simulations. I summarize the status of lattice QCD at finite chemical potential —locating the critical end-point in the QCD phase diagram, predicting event-to-event fluctuation rates of conserved quantities, and finding the rate of strangeness production.     

Dijet production at large rapidity separation in N = 4 supersymmetric Yang-Mills theory

Ratios of azimuthal angle correlations between two jets produced at large rapidity separation are studied in the N = 4 maximally supersymmetric Yang-Mills (MSYM) theory. It is shown that these observables, which directly prove the SL(2,C) symmetry present in gauge theories in the Regge limit, exhibit an excellent perturbative convergence. They are compared to those calculated in QCD for different renormalization schemes concluding that the momentum-substraction scheme with the Brodsky-Lepage-Mackenzie scale-fixing procedure captures the bulk of the MSYM results.     

Percolation transition in Yang-Mills matter at a finite number of colors

We examine baryonic matter at a quark chemical potential of the order of the confinement scale μ(q)～Λ(QCD). In this regime, quarks are supposed to be confined but baryons are close to the "tightly packed limit" where they nearly overlap in configuration space. We show that this system will exhibit a percolation phase transition when varied in the number of colors N(c): at high N(c), large distance correlations at the quark level are possible even if the quarks are essentially confined. At low N(c), this does not happen. We discuss the relevance of this for dense nuclear matter, and argue that our results suggest a new "phase transition," varying N(c) at constant μ(q).     

Chiral magnetic effect in lattice QCD with a chiral chemical potential

We perform a first lattice QCD simulation including a two-flavor dynamical fermion with a chiral chemical potential. Because the chiral chemical potential gives rise to no sign problem, we can exactly analyze a chirally imbalanced QCD matter by Monte Carlo simulation. By applying an external magnetic field to this system, we obtain a finite induced current along the magnetic field, which corresponds to the chiral magnetic effect. The obtained induced current is proportional to the magnetic field and to the chiral chemical potential, which is consistent with an analytical prediction.     

Nucleon–nucleon scattering observables in large-Nc QCD

Nucleon–nucleon scattering observables are considered in the context of the large N_c limit of QCD for initial states with moderately high momenta (pN_c). The scattering is studied in the framework of the time-dependent mean-field approximation. We focus on the dependence of those observables on the spin and isospin of the initial state which may be computed using time-dependent mean-field theory. We show that, up to corrections, all such observables must be invariant under simultaneous spin and isospin flips (i.e., rotations through π/2 in both spin and isospin) acting on either particle. All observables of this class obtained from spin unpolarized measurements must be isospin independent up to 1/N_c corrections. Moreover, it can be shown that the leading correction is of relative order 1/N_c² rather than 1/N_c.     

Parton physics from large-momentum effective field theory

Parton physics,when formulated as light-front correlations,are difficult to study non-perturbatively,despite the promise of lightfront quantization.Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture of a hadron moving at asymptotically large momentum.Here I formulate the approach in the language of an effective field theory for a large hadron momentum P in lattice QCD,LaMET for short.I show that using this new effective theory,parton properties,including light-front parton wave functions,can be extracted from lattice observables in a systematic expansion of 1/P,much like that the parton distributions can be extracted from the hard scattering data at momentum scales of a few GeV.