A Recursive Method to Calculate UV-divergent Parts at One-Loop Level in Dimensional Regularization

A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which involve no other momentum scales except the loop momentum itself. The method can be easily implemented in any symbolic computer language, and an implementation in Mathematica is ready to use.Comment: 10 pages, 1 figure, typos fixed, to appear in Computer Physics Communication

Electroweak Instantons, Axions, and the Cosmological Constant

If there is explicit violation of baryon plus lepton number at some energy scale, then the electroweak theory depends upon a {\theta}-angle. Due to a singular integration over small scale size instantons, this {\theta}-dependence is sensitive to very high momentum scales. Assuming that there is no new physics between the electroweak and Planck scales, for an electroweak axion the energy difference between the vacuum at {\theta} /= 0, and that at {\theta} = 0, is of the correct order of magnitude to be the dark energy observed in the present epoch.Comment: 6 pages, 1 figure; N_h is corrected; minor corrections in the tex

Short Distance Freedom of Quantum Gravity

Fourth order derivative gravity in 3+1-dimensions is perturbatively renormalizable and is shown to describe a unitary theory of gravitons in a limited coupling parameter space. The running gravitational constant which includes graviton contribution is computed. Generically, gravitational Newton's constant vanishes at short distances in this perturbatively renormalizable and unitary theory.Comment: 8 pages, 2 figures, abstract modified, a paragraph added, new references added, typos corrected, version to appear in Physics Letter

Do we need Feynman diagrams for higher orders perturbation theory?

We compute the two and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.Comment: version published in Phys. Lett.

Three Generations in Minimally Extended Standard Models

We present a class of minimally extended standard models with the gauge group $SU(3)_C \times SU(N)_L \times U(1)_X$ where for all $N \geq 3$, anomaly cancelation requires three generations. At low energy, we recover the Standard Model (SM), while at higher energies, there must exist quarks, leptons and gauge bosons with electric charges shifted from their SM values by integer multiples of the electron charge up to $\pm [N/2] e$. Since the value N=5 is the highest $N$ consistent with QCD asymptotic freedom, we elaborate on the 3-5-1 model.Comment: 9 pages, v3: version to appear in PL

Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching

We argue that when conformal symmetry is spontaneously broken the trace anomalies in the broken and unbroken phases are matched. This puts strong constraints on the various couplings of the dilaton. Using the uniqueness of the effective action for the Goldstone supermultiplet for broken ${\cal N}=1$ superconformal symmetry the dilaton effective action is calculated.Comment: 29 pages, 2 figure

Monopoles, confinement and charge localization in the t-J model with dilute holes

We present a quantum field theoretic description on the t$-$J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essentially rooted in intrinsic Mott physics of the t$-$J model. Finally, a finite-temperature phase diagram is proposed. The metal-insulator transition observed in in-plane resistivity measurement is identified to a confinement-deconfinement transition from the perspective of gauge theory. The transition is characterized by the order parameter "Polyakov-line".Comment: 8 papges, 1 figure, accepted by Nucl. Phys.

Positive cosmological constant, non-local gravity and horizon entropy

We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant $\Lambda>0$ and with zero $\Lambda$. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive $\Lambda$, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.Comment: 17 pages, two footnotes added, final version to appear in Nucl.Phys.

Interweaving Chiral Spirals

We elaborate how to construct interweaving chiral spirals in (2+1) dimensions, defined as a superposition of chiral spirals oriented in different directions. We divide a two-dimensional Fermi sea into distinct wedges, characterized by the opening angle 2Theta and depth Q ~ pF, where pF is the Fermi momentum. In each wedge, the energy is lowered by forming a single chiral spiral. The optimal values for Theta and Q are chosen by balancing this gain in energy versus the cost of deforming the Fermi surface (which dominates at large Theta) and patch-patch interactions (dominant at small Theta). Using a non-local four-Fermi interaction model, we estimate the gain and cost in energy by expanding in terms of 1/Nc (where Nc is the number of colors), lqcd/Q, and Theta. Due to a form factor in our non-local model, at small 1/Nc the mass gap (chiral condensate) is large, and the interaction among quarks and the condensate local in momentum space. Consequently, interactions between different patches are localized near their boundaries, and it is simple to embed many chiral spirals. We identify the dominant and subdominant terms at high density and categorize formulate an expansion in terms of lqcd/Q or Theta. The kinetic term in the transverse directions is subdominant, so that techniques from (1+1)-dimensional systems can be utilized. To leading order in 1/Nc and lqcd/Q, the total gain in energy is ~ pF lqcd^2 with Theta ~ (lqcd/pF)^{3/5}. Since Theta decreases with increasing pF, there should be phase transitions associated with the change in the wedge number. We also argue the effects of subdominant terms at lower density where the large-Nc approximation is more reliable.Comment: 54 pages, 21 figures, published versio

Non-Abelian confinement and the dual gauge symmetry: Many faces of flavor symmetry

We review the physics of confinement based on non-Abelian dual superconductor picture, relying on exact solutions in N=2 supersymmetric QCD and based on the recent developments in our understanding of non-Abelian vortices and monopoles. The non-Abelian monopoles, though they are basically just the 't Hooft-Polyakov SU(2) monopoles embedded in various corners of the larger gauge group, require flavor symmetry in an essential way for their very existence. The phenomenon of flavor-color-flavor separation characterizes the multiple roles flavor symmetry plays in producing quantum-mechanical non-Abelian monopoles.Comment: Latex 10 pages, 1 figur