Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

Aspects of effective action for super Chern-Simons-Matter models

We develop the superfield background field method and study the effective action in the N = 2, d3 supersymmetric Chern-Simons-matter systems. The one-loop low-energy effective action for non-Abelian supersymmetric Chern-Simons theory is computed to order F ⁴ by use of N = 2 superfield heat kernel techniques.     

A Chern-Simons effective field theory for the Pfaffian quantum Hall state

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)₂ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.     

Systematic effective field theory investigation of spiral phases in hole-doped antiferromagnets on the honeycomb lattice

Motivated by possible applications to the antiferromagnetic precursor of the high-temperature superconductor Na_xCoO₂.yH₂O, we use a systematic low-energy effective field theory for magnons and holes to study different phases of doped antiferromagnets on the honeycomb lattice. The effective action contains a leading single-derivative term, similar to the Shraiman-Siggia term in the square lattice case, which gives rise to spirals in the staggered magnetization. Depending on the values of the low-energy parameters, either a homogeneous phase with four or a spiral phase with two filled hole pockets is energetically favored. Unlike in the square lattice case, at leading order the effective action has an accidental continuous spatial rotation symmetry. Consequently, the spiral may point in any direction and is not necessarily aligned with a lattice direction.     

World-volume action for fractional branes

We study the world-volume action of fractional Dp-branes of type IIA string theory compactified on the orbifold T⁴/Z₂. The geometric relation between these branes and wrapped branes is investigated using conformal techniques. In particular we examine in detail various scattering amplitudes and find that the leading low-energy interactions are consistent with the boundary action derived geometrically.     

Reentrant violation of special relativity in the low-energy corner

In the effective relativistic quantum field theories, the energy region in which special relativity holds can be sandwiched from both the high-and low-energy sides by domains where special relativity is violated. An example is provided by ³He-A, where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of special relativity in the ultralow-energy corner is accompanied by the redistribution of the momentum-space topological charges among the fermionic flavors. At this ultralow energy, an exotic massless fermion with topological charge N ₃=2 arises whose energy spectrum mixes classical and relativistic behaviors. This effect can lead to neutrino oscillations, if neutrino flavors are still massless on this energy scale.     

Effective lagrangian for supersymmetric theories with intermediate breaking scale

We investigate effective lagrangians in supersymmetric models broken spontaneously at an intermediate energy (～ μ ? M_GUT). It is shown to all orders in perturbation theory that the low-energy interactions of light particles are described by an effective lagrangian with explicit but soft supersymmetry breaking of order μ² / M_GUT.     

Low-energy impact of a heavy Higgs boson sector

The effective theory which characterizes the low-energy sensitivity of the minimal Weinberg-Salam model to a heavy Higgs boson sector is shown to be the gauged SU(2)_L × U(1) non-linear θ model. This theory is the limit of the Weinberg-Salam model as the Higgs boson mass, M_H, is removed (M_H → ∞). Using the symmetry properties of the non-linear theory, along with a power-counting analysis, we are able to classify low-energy observables according to their sensitivity to the regulator (M_H). At one loop, the greatest sensitivity is a logarithmic dependence on the Higgs boson mass. The M_H dependent corrections to some specific, experimentally accessible observables are calculated, and other possible applications of this technique are discussed.     

Threshold effects in open-string theory

We analyze the one-loop effective gauge-field action in Z₂-orbifold compactifications of type-I theory. We show how, for non-abelian group factors, the threshold effects are ultraviolet finite though given entirely by a six-dimensional field theory expression.     

On the relativistic field theory model of the deuteron II

The relativistic field theory model of the deuteron suggested previously is revised and applied to the calculation of the cross sections of the low-energ radiative neutron-proton capture n + p → D + γ and the low-energy two-proton fusion p + p → D + e⁺ + ν_e. For the low-energy data and the potential model prediction. In the case of the two-proton fusion the cross section obtained is 2.9 times as much as that given by the potential approach. The obtained result is discussed in connection with the solar neutrino problem.     

Complex-mass renormalization in chiral effective field theory

We consider a low-energy effective field theory of vector mesons and Goldstone bosons using the complex-mass renormalization. As an application we calculate the mass and the width of the ρ meson.     

Comments on intermediate-scale models

Some superstring-inspired models employ intermediate scales m₁ of gauge symmetry breaking. Such scales should exceed 10¹⁶ GeV in order to avoid prima facie problems with baryon decay through heavy particles and non-perturbative behaviour of the gauge couplings above m_I. However, the intermediate-scale phase transition does not occur until the temperature of the Universe falls below O(m_w), after which an enormous excess of entropy is generated. Moreover, gauge symmetry breaking by renormalization group-improved radiative corrections is inapplicable because the symmetry-breaking field has no renormalizable interactions at scales below m_I. We also comment on the danger of baryon and lepton number violation in the effective low-energy theory.     

N = 4 SYM low-energy effective action in N = 4 harmonic superspace

We apply the N = 4 harmonic superspace with USp(4) harmonic variables for describing the N = 4 SYM low-energy effective action. Scale invariance and gauge symmetry fix the leading term in the low-energy effective action uniquely, up to a constant. The value of the remaining constant can be fixed by the topological quantization condition for the Wess-Zumino term which is present in the component structure of this action.     

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

A Toy Model of the M5-Brane: Anomalies of Monopole Strings in Five Dimensions

We study a five-dimensional field theory which contains a monopole (string) solution with chiral fermion zero modes. This monostring solution is a close analog of the fivebrane solution of M-theory. The cancellation of normal bundle anomalies parallels that for the M-theory fivebrane; in particular, the presence of a Chern-Simons term in the low-energy effective U(1) gauge theory plays a central role. We comment on the relationship between the microscopic analysis of the world-volume theory and the low-energy analysis and draw some cautionary lessons for M-theory.     

Grand unification in RS1

We study unification in the Randall-Sundrum scenario for solving the hierarchy problem, with gauge fields and fermions in the bulk. We calculate the one-loop corrected low-energy effective gauge couplings in a unified theory, broken at the scale M_GUT in the bulk. We find that, although this scenario has an extra dimension, there is a robust (calculable in the effective field theory) logarithmic dependence on M_GUT, strongly suggestive of high-scale unification, very much as in the (4D) Standard Model. Moreover, bulk threshold effects are naturally small, but volume-enhanced, so that we can accommodate the measured gauge couplings. We show in detail how excessive proton decay is forbidden by an extra U(1) bulk gauge symmetry. This mechanism requires us to further break the unified group using boundary conditions. A 4D dual interpretation, in the sense of the AdS/CFT correspondence, is provided for all our results. Our results show that an attractive unification mechanism can combine with a non-supersymmetric solution to the hierarchy problem.     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.