World-volume locally supersymmetric Born-Infeld actions

We derive manifestly locally supersymmetric extensions of the Born-Infeld action with p=2. The construction is based on a first order bosonic action for Dp-branes with a generalized Weyl invariance.     

N = 8 supergravity

The complete structure of N = 8 supergravity is presented with an optional local SO(8) invariance. The SO(8) gauge interactions break E₇ invariance, but leave the local SU(8) unaffected. Exploiting E₇ × SU(8) invariance and using explicit lowest order results, we first derive the complete action and transformation laws. Subsequently, we introduce local SO(8) invariance and prove the consistency of the theory. Possible implications of our results are discussed.     

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.     

Wilson fermions in a two-dimensional model

Wilson's action for fermions on a lattice is compared to the continuum action in a model obtained from the chiral Gross-Neveu model by performing a chiral transformation. The local definition of the axial current leads to two anomalies unrelated by the constraint of Lorentz invariance. In the large-N limit, the mass counterterm of the action is determined; this term is unnecessary in the Osterwalder-Seiler regularization. An expansion in the fermion propagator and in the axial current coupling may be formulated and summed to all orders for large N.     

Renormalization of Lorentz non-invariant actions and manifest T-duality

We study general two-dimensional σ-models which do not possess manifest Lorentz invariance. We show how demanding that Lorentz invariance is recovered as an emergent on-shell symmetry constrains these σ-models. The resulting actions have an underlying group-theoretic structure and resemble Poisson–Lie T-duality invariant actions. We consider the one-loop renormalization of these models and show that the quantum Lorentz anomaly is absent. We calculate the running of the couplings in general and show, with certain non-trivial examples, that this agrees with that of the T-dual models obtained classically from the duality invariant action. Hence, in these cases solving constraints before and after quantization are commuting operations.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

New Lagrangians for Bosonic m-branes with vanishing cosmological constant

A class of conformally invariant σ model actions in 2n dimensions is shown to be classically equivalent to the Nambu-Goto action for an extended object, an m-brane (m+1=2n), embedded in a higher dimensional space-time (d⪖m+1). when m is even, a (2n + 1)-dimensional σ model action is also constructed, which is classically equivalent to the Nambu-Goto action, but in this case there is no conformal invariance. In both cases the cosmological constant can be set to zero.     

Non-abelian D = 11 supermembrane

We obtain a U(M) action for super membranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N = 8 supersymmetry arid it corresponds to M parallel supermembranes minimally immersed on the target M g × T ² (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N = 8 SYM in the IR phase for any number of M2-branes.     

SU(2) gauge symmetry and anomaly of the S = 12 antiferromagnetic Heisenberg model in 2 + 1 dimensions

On the basis of the local SU (2) symmetry of the Heisenberg model, we show that the model, in a continuum limit, reduces to a problem of massless fermions coupled to an SU(2) gauge field in three space-time dimensions. The effective gauge field action changes by ± π ⦶ n ⦶ under a large gauge transformation with winding number n. To restore the gauge invariance, a parity- nonconserving, topological term is needed in the effective action. The physical implications are conjectured.     

Geometric derivation of nonlinear sigma model for the 1D antiferromagnet

It is argued that a purely geometric derivation of the long-range action for the 1D antiferromagnet is available in terms of a Kähler potential. The derivation allows for a natural extension to the t-J model. In particular, it follows that a relevant long-wavelength action of the t-J model exhibits at least at the SUSY (J=2t) point the su(2∣1) invariance rather than the so(5) one.     

Flow equations for the relevant part of the pure Yang—Mills action

Wilson’s exact renormalization group equations are derived and integrated for the relevant part of the pure Yang-Mills action. We discuss in detail how modified Slavnov—Taylor identities control the breaking of BRST invariance in the presence of a finite infrared cutoff k through relations among different parameters in the effective action. In particular they imply a nonvanishing gluon mass term for nonvanishing k. The requirement of consistency between the renormalization group flow and the modified Slavnov—Taylor identities allows to control the self—consistency of truncations of the effective action.     

General covariance of the non-abelian DBI-action: checks and balances

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a base-point independence constraint between matrix Riemann normal coordinate systems. First, we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose base-point independence using an auxiliary dN²-dimensional nonlinear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order 4, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.     

关于Noether对称性的两种理解

介绍了对Lagrange系统Noether对称性的两种理解，一种理解为Lagrange函数的不变性，另一种理解为作用量的不变性.研究表明，这两种理解是不同的.在一些条件下，Lagrange函数的不变性可以成为作用量的不变性，在另一些条件下，作用量的不变性可以成为Lagrange函数的不变性.将Noether对称性理解为作用量的不变性是合理的. 关键词： Lagrange系统 Noether对称性 作用量的不变性 Lagrange函数的不变性     

U(1)×SU(2)-gauge invariance of non-relativistic quantum mechanics,and generalized Hall effects

We show that the non-relativistic quantum mechanics of particles with spin coupled to an electromagnetic field has a naturalU(1)×SU(2) gauge invariance. Ward identities reflecting this gauge invariance combined with an assumption of incompressibility of a system of such particles in an appropriate external field and for suitable values of the particle density permit us to determine the form of the effective action of the system as a functional of small fluctuations in the electromagnetic field, in the large-distance-, adiabatic limit. In this limit, the action is found to have a universal form. We present explicit results for two-dimensional, incompressible electron fluids and apply them to derive the equations of linear response theory, describing a variety of generalized Hall effects. Sum rules for the Hall conductivities, magnetic susceptibilities and other quantities of physical interest are found.     

Hadron spectrum in a Euclidean invariant regularization of QCD at strong coupling

A new random lattice regularization, which preserves exact euclidean invariance, is proposed for QCD. The corresponding action couples any two points on the random lattice with a gaussian damping of range b in the euclidean distance of the points. This property, which avoids the introduction of the concept of nearest neighbours on a random lattice, greatly simplifies computations of physical observables with respect to the situation of the standard random lattice models. The present calculation of the hadron spectrum of a SU(N = 3) gauge model is performed at strong coupling β = 0, at leading order in 1/N and in the inverse lattice point density ?. The results for mesons of definite spin-parity and flavor are quite good; the results for the baryons are, as usual, less satisfying (small N-Δ mass difference), but are also expected to be less reliable in our approximations. The problem of the regularization of chiral fermions is not settled in this paper where the used approximations yield a massless η-boson.     

A dislocation kinetic model of the formation and propagation of intense shock waves in crystals

Analytical expressions for the front of a shock plastic wave and the plastic relaxation region behind the front have been obtained and a relation of the wave parameters to the pressure in the wave has been determined in the framework of the dislocation kinetic approach based on kinetic relationships and equations for the density of dislocations. Within this approach, the physical mechanism of the origin and the universality of the Swegle-Grady empirical relationship for crystals in the form of a power-law dependence of the plastic strain rate $\dot \varepsilon $ on the pressure in the wave P, that is, $\dot \varepsilon $ ～ P ⁴, have been discussed. The principal contribution to this dependence comes from the power-law (cubic) dependence of the density of dislocations generated in the wave front on the pressure. The universality of the Swegle-Grady relationship is based on the invariance of the dissipative action A. An explicit expression for the dissipative action has been derived: A = SBV ₀/3β. As follows from this expression, the dissipative action is determined by fundamental parameters for shock wave loading of crystals, such as the dislocation viscous drag coefficient B and the adiabaticity factor S (here, V ₀ is the specific volume and β is a coefficient of the order of 10^?3–10^?2). In light of the revealed circumstances, such phenomenological notions as the Hugoniot elastic limit and the elastic precursor have been critically examined.     

The contribution of theC-field to the action functional

It is shown that the action of the usual field theory requires the inclusion of two terms in order to be equivalent, in the macroscopic case, to the action proposed by Hoyle & Narlikar (1964c). These actions correspond only to a modified form of Maxwell's equations, which, in consequence, lose their property of conformal invariance. It is also demonstrated how theC-field and electromagnetic field can be brought into unison by an appropriate re-definition of the vector potential. Both field theories can thus be described in terms of one vector Green's function.     

Semi-relativistic charge-current density operator

The charge-current density and two-photon operators consistent with a single-particle semirelativistic Hamiltonian are derived within a suitable functional derivative formalism which preserves gauge invariance. An application to electron scattering is presented and results are compared with a fully relativistic case and the non-relativistic cases corrected through fourth order in M⁻¹.     

Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B∧F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci–Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.