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Register a new userDuality Invariance and Higher Derivatives
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We dimensionally reduce the spacetime action of bosonic string theory, and that of the bosonic sector of heterotic string theory after truncating the Yang-Mills gauge fields, on a $d$-dimensional torus including all higher-derivative corrections to first order in $alpha$. A systematic procedure is developed that brings this action into a minimal form in which all fields except the metric carry only first order derivatives. This action is shown to be invariant under ${rm O}(d,d,mathbb{R})$ transformations that acquire $alpha$-corrections through a Green-Schwarz type mechanism. We prove that, up to a global pre-factor, the first order $alpha$-corrections are uniquely determined by ${rm O}(d,d,mathbb{R})$ invariance.
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We present new models of non-linear electromagnetism which satisfy the Noether-Gaillard-Zumino current conservation and are, therefore, self-dual. The new models differ from the Born-Infeld-type models in that they deform the Maxwell theory starting with terms like $lambda (partial F)^{4}$. We provide a recursive algorithm to find all higher order terms in the action of the form $lambda^{n} partial ^{4n} F^{2n+2} $, which are necessary for the U(1) duality current conservation. We use one of these models to find a self-dual completion of the $lambda (partial F)^{4}$ correction to the open string action. We discuss the implication of these findings for the issue of UV finiteness of ${cal N}=8$ supergravity.
We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second cohomology class. We find the explicit T-duality transformation that acts locally on the supermembrane theory and we show that it is an exact symmetry of the theory. We give a global interpretation of the T-duality in terms of bundles. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. We show that in the limit when the torus degenerate into a circle and the M2 mass operator restricts to the string-like configurations, the usual closed string T-duality transformation between the type IIA and type IIB mass operators is recovered. Moreover if we just restrict M2 mass operator to string-like configurations but we perform a generalized T-duality we find the SL(2,Z) non-perturbative multiplet of IIA.
In both ${cal N}=1$ and ${cal N}=2$ supersymmetry, it is known that $mathsf{Sp}(2n, {mathbb R})$ is the maximal duality group of $n$ vector multiplets coupled to chiral scalar multiplets $tau (x,theta) $ that parametrise the Hermitian symmetric space $mathsf{Sp}(2n, {mathbb R})/ mathsf{U}(n)$. If the coupling to $tau$ is introduced for $n$ superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action $Gamma [tau, bar tau]$ with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid $mathsf{Sp}(2n, {mathbb R})$ transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the ${cal N}=1$ and ${cal N}=2$ locally supersymmetric induced actions which determine the logarithmically divergent parts of the corresponding effective actions. In the ${cal N}=1$ case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet $(n=1)$ coupled to a chiral dilaton-axion multiplet. We also describe the general structure of ${cal N}=1$ super-Weyl anomalies that contain weight-zero chiral scalar multiplets $Phi^I$ taking values in a Kahler manifold. Explicit anomaly calculations are carried out in the $n=1$ case.
The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between locality,gauge,Lorentz and conformal invariance require- ments. Improved traceless stress tensors are then constructed;each violates one of the above criteria.However,when d=N+2,there is a duality equivalence between N-form models and massless scalars.Here we show that conformal invariance is not lost,by constructing a quasilocal gauge invariant improved stress tensor.The correlators of the scalar theory are then reproduced,including the latters trace anomaly.
We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables and show the possibility to evade the Ostrogradsky instability when the Lagrangian is degenerate, still in the context of classical mechanics. In particular, we explain why higher-derivatives Lagrangians and/or higher-derivatives Euler-Lagrange equations do not necessarily lead to the propagation of an Ostrogradsky ghost. We also study some quantum aspects and illustrate how the Ostrogradsky instability shows up at the quantum level. Finally, we generalize our analysis to the case of higher order covariant theories where, as the Hamiltonian is vanishing and thus bounded, the question of Ostrogradsky instabilities is subtler.
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