On the relation between effective supersymmetric actions in different dimensions

We make two remarks: (i) Renormalization of the effective charge in a four-dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua of the corresponding reduced quantum-mechanical system. Supersymmetry provides constraints for possible modifications of the metric, and this gives us a simple proof of nonrenormalization theorems for the original four-dimensional theory. (ii) We establish a nontrivial relationship between the effective (0 + 1)-dimensional and (1 + 1)-dimensional Lagrangians. (The latter represent conventional Kählerian σ models.)     

Chiral anomalies in even and odd dimensions

Odd dimensional Yang-Mills theories with an extra topological mass term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.     

The chiral anomaly and goldstone-wilczek current in even dimensions

The form of the non-abelian anomaly is described in arbitrary even dimension when the gauge group contains explicit U(1) factors. An effective action is constructed which when varied under the group reproduces the anomaly. It constitutes a generalization of the Wess-Zumino action.     

Extended Skyrme models in even dimensions and higher-dimensional solitons

We propose a higher-dimensional soliton model — an extended Skyrme model — in an even-dimensional spacetime. A hedgehog ansatz is also generalized to higher-dimensional cases and it is found that the soliton generally has the fermion number, i.e., the topological soliton.Fellow of Yukawa Foundation.     

Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction

An exploratory study of chiral four-nucleon interactions in nuclear and neutron matter is performed. The leading-order terms arising from pion-exchange in combination with the chiral 4??-vertex and the chiral NN3??-vertex are found to be very small. Their attractive contribution to the energy per particle stays below 0.6 MeV in magnitude for densities up to ?? = 0.4 fm^?3. We consider also the four-nucleon interaction induced by pion-exchange and twofold ??-isobar excitation of nucleons. For most of the closed four-loop diagrams the occurring integrals over four Fermi spheres can either be solved analytically or reduced to easily manageable one- or two-parameter integrals. After summing the individually large contributions from 3-ring, 2-ring and 1-ring diagrams of alternating signs, one obtains at nuclear matter saturation density ?? ₀ = 0.16 fm^?3 a moderate contribution of 2.35 MeV to the energy per particle. The curve $\bar E(\rho )$ rises rapidly with density, approximately with the third power of ??. In pure neutron matter the analogous chiral four-body interactions lead, at the same density ?? _n , to a repulsive contribution that is about half as strong. The present calculation indicates that long-range multi-nucleon forces, in particular those provided by the strongly coupled ??N??-system with its small mass-gap of 293 MeV, can still play an appreciable role for the equation of state of nuclear and neutron matter.     

Gravitational actions in two dimensions and the Mabuchi functional

The Mabuchi energy is an interesting geometric functional on the space of Kähler metrics that plays a crucial rôle in the study of the geometry of Kähler manifolds. We show that this functional, as well as other related geometric actions, contribute to the effective gravitational action when a massive scalar field is coupled to gravity in two dimensions in a small mass expansion. This yields new theories of two-dimensional quantum gravity generalizing the standard Liouville models.     

Extended skyrme models in even dimensions and higher-dimensional solitons II: Wess-Zumino terms in two and higher dimensions

We investigate Wess-Zumino terms in higher-dimensional nonlinear sigma models using the higher-dimensional hedgehog ansatz proposed by us. The gauged Wess-Zumino terms are also calculated from a fermion determinant, and we comment on extended objects or a dibaryon ansatz.Partially supported by the Grant-in-Aid for Scientific Research, No. 61460005.     

Combustion waves in two dimensions and their one-dimensional approximation

A two-dimensional reaction - diffusion system, describing combustion waves in a fuel layer or cylinder is studied. The results are compared with those obtained from a one-dimensional approximate model, where the approximation is motivated by centre manifold reduction.

From the comparison it is clear that the one-dimensional approximation is accurate when the heat loss from the layer to the environment is not too large or when the layer is large enough such that the one-dimensional adiabatic approximation is appropriate. This is usually the case in experimental work, but it is not necessarily appropriate to asymptotic calculations. Differences between the one- and two-dimensional models in the size of the layer leading to quenching of the combustion are seen to be significant for certain values of the fuel parameter and heat loss.     

Elliptic index and superstring effective actions

Certain N = 1 supersymmetric string one-loop effective actions can be obtained directly from the path integral. As the computation is essentially the same as the one leading to the index of the Dirac-Ramond operator, they are determined by the gauge and gravitational anomaly structure of the theory. Specifically, we calculate the four-point effective action in ten dimensions, the corrections to the kinetic terms in d = 6 (including auxiliary fields) and the Fayet-Iliopoulos D-term in d = 4. We also compute the β-function of four-dimensional N = 2 theories from the elliptic genus in d = 6. Furthermore, we derive supersymmetry Ward type identities in terms of Kac-Moody characters, relating parity conserving with parity violating amplitudes.     

Off-shell effective actions in string theory

A new, “off-shell”, approach to conformal invariance, β-functions and field equations in first quantized string theory is presented. The method, valid to all orders in the weak-field expansion and non-perturbatively in α′, is illustrated for a tachyon background at genus zero and one level. For a particular choice, we derive a Zamolodchikov-type equation for the effective action.     

On matrix geometry and effective actions

We provide an elementary systematic discussion of single-trace matrix actions and of the group of matrix reparameterization that acts on them. The action of this group yields a generalized notion of gauge invariance which encompasses ordinary diffeomorphism and gauge invariances. We apply the formalism to non-abelian D-brane actions in arbitrary supergravity backgrounds, providing in particular explicit checks of the consistency of Myers? formulas with supergravity gauge invariances. We also draw interesting consequences for emergent space models based on the study of matrix effective actions. For example, in the case of the _AdS5×S⁵${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ background, we explain how the standard tensor transformation laws of the supergravity fields under ordinary diffeomorphisms emerge from the D-instanton effective action in this background.     

Dynamics and effective actions of BCS superconductors

We derive the effective dynamical theory for BCS superconductors, based on the effective action formalism. Both the metallic regime and the superconducting regime are studied in the clean and dirty limit. The full electrodynamics of the problem is formulated in a manifestly gauge-invariant and transparent way. Furthermore, we consider the effect of particle-hole asymmetry in the band structure, and discuss its consequences for vortex dynamics and the topological term in the effective action. The effective action is the starting point for treating (quantum-) dynamical problems involving BCS superconductors. Received 23 November 1998     

On the superfield effective potential in three dimensions

We develop the superfield approach to the effective potential in three dimensions and calculate the one-loop and two-loop Kählerian effective potential in commutative and noncommutative cases.     

Local density approximation in effective density-dependentαN-interactions

Different forms of a local density approximation (LDA) in effective density-dependent αN-interactions are compared in single-folding optical model analyses of elastic α particle scattering by^{40, 42, 44, 48}Ca atE _α=104 MeV and by⁴⁰Ca atE _α=140 MeV. It is shown that the form of the LDA considerably influences the results on folded optical potentials. A variable form of the LDA is suggested and discussed which includes previous forms as limiting cases. The new form leads to better fits to the data and to full consistency with the best available “model-independent” optical potentials.     

Parity violation and the effective gravitational action in three dimensions

A diagrammatic computation of the parity-breaking gravitational effective action induced by massless fermions in three dimensions is presented. The lowest-order approximation to the Chern-Simons action is obtained, in agreement with a general index-theoretic result.