As an extension of the Ivanov-Zupnik approach to self-dual nonlinear electrodynamics in four dimensions [1,2], we reformulate U(1) duality-invariant nonlinear models for a gauge $(2p-1)$-form in $d=4p$ dimensions as field theories with manifestly U(1) invariant self-interactions. This reformulation is suitable to generate arbitrary duality-invariant nonlinear systems including those with higher derivatives.
We present a new class of matrix models which are manifestly symmetric under the T-duality transformation of the target space. The models may serve as a nonperturbative regularization for the T-duality symmetry in continuum string theory. In particular, it now becomes possible to extract winding modes explicitly in terms of extended matrix variables.
A way of covariantizing duality symmetric actions is proposed. As examples considered are a manifestly space-time invariant duality--symmetric action for abelian gauge fields coupled to axion-dilaton fields and gravity in D=4, and a Lorentz-invariant action for chiral bosons in D=2. The latter is shown to admit a manifestly supersymmetric generalization for describing chiral superfields in n=(1,0) D=2 superspace.
In this paper, we will investigate a manifestly $SL(2,R)$-invariant structure for the energy-momentum tensor of ModMax theory as a nonlinear modification of Maxwell electrodynamics which includes conformal invariance as well. In the context of this theory, we show that the energy-momentum tensor of the generalized Born-Infeld theory can also be written in the same invariant form. We will find manifestly self-dual invariant actions corresponding to the invariant couplings $λ$ and $γ$ in these theories. It can be shown that the resultant actions correspond to the irrelevant and marginal $T\bar{T…
We present a manifestly duality covariant formulation of the composite non-BPS and almost-BPS systems of multi-centre black hole solutions in four dimensions. The method of nilpotent orbits is used to define the two systems in terms of first order flow equations that transform covariantly under the duality group. Subsequently, we rewrite both systems of equations in terms of real, manifestly duality covariant, linear systems of Poisson equations. Somewhat unexpectedly, we find that the two systems are naturally described by the same equations involving space dependent abelian isometries that a…
The free action for massless Ramond-Ramond fields is derived from closed superstring field theory using the techniques of Siegel and Zwiebach. For the uncompactified Type IIB superstring, this gives a manifestly Lorentz-covariant action for a self-dual five-form field strength. Upon compactification to four dimensions, the action depends on a U(1) field strength from 4D N=2 supergravity. However, unlike the standard Maxwell action, this action is manifestly invariant under the electromagnetic duality transformation which rotates $F_{mn}$ into $ε_{mnpq} F^{pq}$.
We investigate how SL(2,Z) duality is realized in nonrelativistic type IIB superstring theory, which is a self-contained corner of relativistic string theory. Within this corner, we realize manifestly SL(2,Z)-invariant (p,q)-string actions. The construction of these actions imposes a branching between strings of opposite charges associated with the two-form fields. The branch point is determined by these charges and the axion background field. Both branches must be incorporated in order to realize the full SL(2,Z) group. Besides these string actions, we also construct D-instanton and D3-brane …
The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is manifestly invariant under duality rotations in the internal 2-plane of the spacetime curvature and its dual. In order to achieve this manifestly duality-invariant form, it is necessary to introduce two "prepotentials", which form a duality multiplet. These prepotentials enjoy interesting gauge invariance symmetries, which are, for each, linearized diffeomorphi…
We give a manifestly U-duality invariant formula for the degeneracy of 1/8 BPS dyons in type II string theory on T^6 for a U-duality invariant subset of charge vectors. Besides depending on the Cremmer-Julia invariant the degeneracy also depends on other discrete invariants of E_{7(7)}(Z).
We derive a manifestly duality-invariant formulation of the action principle for linearized gravity on anti de Sitter background. The analysis is based on the two-potential formalism, obtained upon resolution of the constraints in the Hamiltonian formulation. We discuss the relevance of our result in the context of holography.
A manifestly Lorentz and diffeomorphism invariant form for the abelian gauge field action with local duality symmetry of Schwarz and Sen is given. Some of the underlying symmetries of the covariant action are further considered. The Noether conserved charge under continuous local duality rotations is found. The covariant couplings with gravity and the axidilaton field are discussed.
Loop-Tree Duality (LTD) is a framework in which the energy components of all loop momenta of a Feynman integral are integrated out using residue theorem, resulting in a sum over tree-like structures. Originally, the LTD expression exhibits cancellations of non-causal thresholds between summands, also known as dual cancellations. As a result, the expression exhibits numerical instabilities in the vicinity of non-causal thresholds and for large loop momenta. In this work we derive a novel, generically applicable, Manifestly Causal LTD (cLTD) representation whose only thresholds are causal thresh…
We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST-mechanism. The dynamics for classical point particles is described by an action functional living on a circle, if the Dirac-Schwinger quantization condition for electric and magnetic charges holds. The inconsistent classical field theory depends on an arbitrary, but fixed, external vector field, a generalization of the Dirac-string. Nevertheless, the Quantum Field Theory, obtained from this cla…
We give the manifestly T-dual formulation of the massless sector of the classical 3D Type II superstring in off-shell 3D N=2 superspace, including the action. It has a simple relation to the known superspace of 4D N=1 supergravity in 4D M-theory via 5D F-theory. The pre potential appears as part of the vielbein, without derivatives.
A manifestly U-duality covariant approach to M-theory cosmology is developed and applied to cosmologies in dimensions D=4,5. Cosmological properties such as expansion powers and Hubble parameters turn out to be U-duality invariant in certain asymptotic regions. U-duality transformations acting on cosmological solutions, on the other hand, shift the transition time between two asymptotic regions and determine the details of the transition. Moreover, in D=5, we show that U-duality can map expanding negative and positive branch solutions into each other.
The duality symmetric but not manifestly covariant action proposed by Schwarz-Sen is canonically quantized in the Coulomb gauge. The resulting theory turns out to be, nevertheless, relativistically invariant. It is shown, afterwards, that the Schwarz-Sen model naturally emerges when duality is implemented as a local symmetry of sourceless electrodynamics. This implies in the equivalence of these theories at the quantum level.
We consider duality transformations in N=2 Yang--Mills theory coupled to N=2 supergravity, in a manifestly symplectic and coordinate covariant setting. We give the essential of the geometrical framework which allows one to discuss stringy classical and quantum monodromies, the form of the spectrum of BPS saturated states and the Picard--Fuchs identities encoded in the special geometry of N=2 supergravity theories.
We prove that a sum of free non-covariant duality-symmetric actions does not allow consistent, continuous and local self-interactions that deform the gauge transformations. For instance, non-Abelian deformations are not allowed, even in 4 dimensions where Yang-Mills type interactions of 1-forms are allowed in the non-manifestly duality-symmetric formulation. This suggests that non-Abelian duality should require to leave the standard formalism of perturbative local field theories. The analyticity of self-interactions for a single duality-symmetric gauge field in four dimensions is also analyzed…
We present a manifestly Lorentz invariant and supersymmetric component field action for $D = 10$, type $IIB$ supergravity, using a newly developed method for the construction of actions with chiral bosons, which implies only a single scalar non propagating auxiliary field. With the same method we construct also an action in which the complex two-form gauge potential and its Hodge-dual, a complex six-form gauge potential, appear in a symmetric way in compatibility with supersymmetry and Lorentz invariance. The duals of the two physical scalars of the theory turn out to be described by a $SL(2,R…
Worldsheet supersymmetric string action is written in duality invariant form for flat as well as curved backgrounds. First the action in flat backgrounds is written by introducing auxiliary fields. We also give the superfield form of this action and obtain the offshell supersymmetry algebra. The action has a modified Lorentz invariance and supersymmetry and reduces to the usual form when the auxiliary fields are eliminated using their equations of motion. Supersymmetric nonlinear sigma model in curved backgrounds is also written in manifestly duality invariant form when the background metric a…
Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to more general Lorentz representations than solely the spinorial and vectorial ones of standard lore. Such superspaces provide model configuration spaces for theories of arbitrary spin fields. Our framework is an elegant one for handling higher-dimensional theories in a manifestly SO(3,1) covariant fashion. A further application is the construction of a hierarch…
For the SL(2,\textbf{R}) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials $A^μ$ and $B^μ$ in a judicious way. On the two potentials $A^μ$ and $B^μ$ the SL(2,\textbf{R}) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,\textbf{Z})-invariant action. Also given is a Zwanziger-type action for SL(2,\textbf{R}) duality-invariant B…
A manifestly S-dual, and `12 dimensional', IIB superstring action with an $Sl(2;\bR)$ doublet of `Born-Infeld' fields is presented. The M-theory origin of the 12th dimension is the M-2-brane tension, which can be regarded as the flux of a 3-form worldvolume field strength. The latter is required by the fact that the M-2-brane can have a boundary on an M-5-brane.
We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all beta, assuming the existence of an interacting Spin(8) invariant fixed point at the origin. The resulting formulae are manifestly invariant under the SL(2,Z) duality of four dimensional N=4 SYM and lead to interesting quantitative predictions for instanton effects in gauge theory and in Type II string theory.
We show that the duality between the self-dual and Maxwell-Chern-Simons theories in 2+1-dimensions survives when the space-time becomes noncommutative. Existence of the Seiberg-Witten map is crucial in the present analysis. It should be noted that the above models, being manifestly gauge variant and invariant respectively, transform differently under the Seiberg-Witten map. We also discuss this duality in the Stuckelberg formalism where the self-dual model is elevated to a gauge theory. The "`master"' lagrangian approach has been followed throughout.
The self-duality of chiral p-forms was originally investigated by Pasti, Sorokin and Tonin in a manifestly Lorentz covariant action with non-polynomial auxiliary fields. The investigation was then extended to other chiral p-form actions. In this paper we point out that the self-duality appears in a wider context of theoretical models that relate to chiral p-forms. We demonstrate this by considering the interacting model of Floreanini-Jackiw chiral bosons and gauge fields, the generalized chiral Schwinger model (GCSM) and the latter's gauge invariant formulation, and discover that the self-dual…
We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of "spectator" fields in this process and also show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double. We then develop the N=(0,1) supersymmetric duality invariant formalism.
In heterotic string theory compactified on T^6, the T-duality orbits of dyons of charge (Q,P) are characterized by O(6,22;R) invariants Q^2, P^2 and Q.P together with a set of invariants of the discrete T-duality group O(6,22;Z). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that for dyons with torsion r, the degeneracy formula, expressed as a function of Q^2, P^2 and Q.P, is required to be manifestly invariant under only a subgroup of the S-duality group. This subgroup is isomorphic …
We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models mimic Dirac-Born-Infeld theory but it is unclear whether they are Lagrangian.
We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the presence of a single auxiliary scalar field. It is shown that the duality-symmetric action should be invariant under the two local symmetries characteristic of this approach, which impose constraints on the form of the action similar to those of Gaillard and Zumino and in the non-covariant formalism. We show that the (twisted) self-duality condition obtained from…
We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2. It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons and (p,q) string instantons wrapping T^2. We provide evidence for this modular form by showing that the coefficients at tree level and at one loop precisely match those obtained using string perturbation theory. Using duality, parts of the perturbative amplitude are also shown to match exactly the results obtained from eleven dimensional supergravity compact…
Cosmological perturbation equations derived from low-energy effective actions are shown to be invariant under a duality transformation reminiscent of electric-magnetic, strong-weak coupling, S-duality. A manifestly duality-invariant approximation for perturbations far outside the horizon is introduced, and it is argued to be useful even during a high curvature epoch. Duality manifests itself through a remnant symmetry acting on the classical moduli of cosmological models, and implying lower bounds on the number and energy density of produced particles.
Double Field Theory is a manifestly T-duality invariant formulation of string theory in which the effective theory at any order of $α'$ is invariant under global $O(D,D)$ transformations and ought to be invariant under gauge transformations which receive $α'$-corrections. On the other hand, the effective theory in the usual $D$-dimensional formulation of string theory is manifestly gauge invariant and ought to be invariant under T-duality transformations which receive $α'$-corrections. We speculate that the combination of these two constraints may fix both the $2D$-dimensional and the $D$-dime…
The collision of plane waves corresponding to massless states of closed string is considered in $D$-dimensional space-time. The reduced tree level effective action is known to be manifestly $O(d,d)$ invariant, $d$ being the number of transverse spatial dimensions in the collision process. We adopt a coset space reformulation of the effective two dimensional theory and discuss the relation of this process with classical integrable systems in two dimensions in the presence of gravity. We show how it is possible to generate new backgrounds for the scattering process, from known background solutio…
We propose a manifestly U-duality invariant modular form for the D^6 R^4 interaction in the effective action of type IIB string theory compactified on T^2. It receives perturbative contributions upto genus three, as well as non-perturbative contributions from D-instantons and (p,q) string instantons wrapping T^2. Our construction is based on constraints coming from string perturbation theory, U-duality, the decompactification limit to ten dimensions, and the equality of the perturbative part of the amplitude in type IIA and type IIB string theories. Using duality, parts of the perturbative amp…
The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space-time covariance is no longer manifest but still present with a non-standard realization of space-time diffeomorphisms on the gauge fields.…
We consider open strings ending on D-branes in the presence of constant metric, G, antisymmetric tensor, B and gauge field, A. The Hamiltonian is manifestly invariant under a global noncompact group; strikingly similar to toroidally compactified closed string Hamiltonian. The evolution equations for the string coordinates, $\{X^i \}$ and their dual partners, $\{Y_i \}$, are combined to obtain equations of motion invariant under the noncompact symmetry transformations. We show that one can start from a noncommutative theory, with nonvanishing G and B and mixed boundary conditions and then go ov…
We systematically apply the formalism of duality walls to study the action of duality transformations on boundary conditions and local and nonlocal operators in two, three, and four-dimensional free field theories. In particular, we construct a large class of D-branes for two-dimensional sigma-models with toroidal targets and determine the action of the T-duality group on it. It is manifest in this formalism that T-duality transformations on D-branes are given by a differential-geometric version of the Fourier-Mukai transform.
Manifestly N=2 supersymmetric Feynman rules are found for different off-shell realizations of the massless hypermultiplet in projective superspace. When we reduce the Feynman rules to an N=1 superspace we obtain the correct component propagators. The Feynman rules are shown to be compatible with a ``duality'' that acts only on the auxiliary fields, as well as with the usual duality relating the hypermultiplet to the tensor multiplet.
In this paper we review some properties of BPS black holes of supergravities with n=32,16 supersymmetries. The BPS condition, a condition on the eigenvalues of the central charge matrix, can be shown to be U-duality invariant. We explicitly work out D=4, N=8 and D=5, N=4 supergravities.
In this paper, we describe non-abelian gauge bundles with magnetic and electric fluxes on higher dimensional noncommutative tori. We give an explicit construction of a large class of bundles with nonzero magnetic 't Hooft fluxes. We discuss Morita equivalence between these bundles. The action of the duality is worked out in detail for the four-torus. As an application, we discuss Born-Infeld on this torus, as a description of compactified string theory. We show that the resulting theory, including the fluctuations, is manifestly invariant under the T-duality group SO(4,4;Z). The U-duality inva…
We analyze non-linear interactions of 2N-form Maxwell fields in a space-time of dimension D=4N. Based on the Pasti-Sorokin-Tonin (PST) method, we derive the general consistency condition for the dynamics to respect both manifest SO(2)-duality invariance and manifest Lorentz invariance. For a generic dimension D=4N, we determine a canonical class of exact solutions of this condition, which represent a generalization of the known non-linear duality invariant Maxwell theories in D=4. The resulting theories are shown to be equivalent to a corresponding class of canonical theories formulated a la G…
We shall discuss issues of duality and topological mass generation in diverse dimensions. Particular emphasis will be given to the mass generation mechanism from interference between self and anti self-dual components, as disclosed by the soldering formalism. This is a gauge embedding procedure derived from an old algorithm of second-class constraint conversion used by the author to approach anomalous gauge theories. The problem of classification of the electromagnetic duality groups, both massless and massive, that is closely related will be discussed. Particular attention will be paid to a n…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an action manifestly invariant under duality rotations in presence of both electric and magnetic external sources. It is also shown how, in the reduced phase-space, all higher spin gauge fields can be written as bi-hamiltonian systems. The role of the second hamiltonian is played by the electromagnetic duality generator. The second part is devoted to the study o…
A closed-form expression is obtained for a holomorphic sector of the two-loop low-energy effective action for the N = 4 super Yang-Mills theory on its Coulomb branch where the gauge group SU(N) is spontaneously broken to SU(N-1) x U(1) and the dynamics is described by a single Abelian N = 2 vector multiplet. In the framework of the background-field method, this holomorphic sector is singled out by computing the effective action for a background N = 2 vector multiplet satisfying a relaxed super self-duality condition. At the two-loop level, the N = 4 SYM effective action is shown to possess no …
We derive the asymptotic symmetries of the manifestly duality invariant formulation of electromagnetism in Minkoswki space. We show that the action is invariant under two algebras of angle-dependent $u(1)$ transformations, one electric and the other magnetic. As in the standard electric formulation, Lorentz invariance requires the addition of additional boundary degrees of freedom at infinity, found here to be of both electric and magnetic types. A notable feature of this duality symmetric formulation, which we comment upon, is that the on-shell values of the zero modes of the gauge generators…
Closed string theory exhibits an O(D,D) duality symmetry on tori, which in double field theory is manifest before compactification. I prove that to first order in $α'$ there is no manifestly background independent and duality invariant formulation of bosonic string theory in terms of metric, b-field and dilaton. To this end I use O(D,D) invariant second order perturbation theory around flat space to show that the unique background independent candidate expression for the gauge algebra at order $α'$ is inconsistent with the Jacobi identity. A background independent formulation exists instead fo…
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of non-compact type, with K the maximal compact subgroup of G(R). In particular, we show how Eisenstein series of the T-duality group SO(d,d,Z) can be used to represent one- and g-loop amplitudes in compactified string theory. We also obtain their non-perturbative extensions in terms of the…
We present the most general family of stationary point-like solutions of pure N=4, d=4 Supergravity characterized by completely independent electric and magnetic charges, mass, angular momentum and NUT charge plus the asymptotic values of the scalars. It includes, for specific values of the charges all previously known BPS and non-BPS, extreme and non-extreme black holes and Taub-NUT solutions. As a family of solutions, it is manifestly invariant under T and S duality transformations and exhibits a structure related to the underlying special geometry structure of the theory. Finally, we study …
A formulation of linearized gravity which is manifestly invariant under electric-magnetic duality rotations in the internal space of the metric and its dual, and which contains both metrics as basic variables (rather than the corresponding prepotentials), is derived. In this bimetric formulation, the variables have a more immediate geometrical significance, but the action is non-local in space, contrary to what occurs in the prepotential formulation. More specifically, one finds that: (i) the kinetic term is non-local in space (but local in time); (ii) the Hamiltonian is local in space and in …
U-duality p-branes in toroidally compactified type II superstring theories in space-time dimensions $10 > D \ge 4$ can be constructed explicitly based on the conjectured U-duality symmetries and the corresponding known single-charge super p-brane configurations. As concrete examples, we first construct explicitly the $SL(3, Z)$ superstrings and $SL(3, Z) \times SL(2, Z)$ 0-branes as well as their corresponding magnetic duals in $D = 8$. For the $SL(3, Z)$ superstrings (3-branes), each of them is characterized by a triplet of integers corresponding to the electric-like (magnetic-like) charges a…
The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper $n_v$ abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to $n_s$ uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by $Sp(2n_v,\mathbb{R})$. The symplectic group mixes its electric and…
We discuss black hole thermodynamics in the manifestly duality invariant formalism of double field theory (DFT). We reformulate and prove the first law of black hole thermodynamics in DFT, using the covariant phase space approach. After splitting the full O(D, D) invariant DFT into a Kaluza-Klein-inspired form where only n coordinates are doubled, our results provide explicit duality invariant mass and entropy formulas. We illustrate how this works by discussing the black fundamental string solution and its T-duals.
Exceptional field theories are the manifestly duality covariant formulations of the target space theories of string/M-theory in the low-energy limit (supergravity) or for certain truncations. These theories feature a rich system of sub-theories, corresponding to different consistent truncations. We review the structure of exceptional field theory and elaborate on various potential applications. In particular, we discuss how exceptional field theories capture some of the the magic supergravity triangles, Hull's $*$-theories related to timelike dualities, as well as the generalized supergravitie…
We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the $SO(2)$ duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to $p$-forms in $2p+2$ dimensio…
We study the compactification of OM-theory on tori and show a simple heuristic derivation of the $S$-duals of noncommutative open string theory in diverse dimensions from the OM-theoretical point of view. In particular, we identify the $S$-duality between noncommutative open string theory and noncommutative Yang-Mills theory in $(3+1)$ dimensions as the exchange of two circles of a torus on which OM-theory is compactified. Also, we briefly discuss $T$-duality between noncommutative open string theories.
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting charged particles. One of the models is manifestly invariant under both Duality and Periodic shifts of the statistical angle and, hence, it has a full Modular Invariance. We derive the transformation laws for the correlation functions under the modular group and use them to derive symmetry constraints for the conductances. These allow us to calculate exactly the c…
