We study the Klein four-group $(K_4)$ symmetry of the time-dependent Schrödinger equation for the conformal mechanics model of de Alfaro-Fubini-Furlan (AFF) with confining harmonic potential and coupling constant $g=ν(ν+1)\geq -1/4$. We show that it undergoes a complete or partial (at half-integer $ν$) breaking on eigenstates of the system, and is the automorphism of the $\mathfrak{osp}(2,2)$ superconformal symmetry in super-extensions of the model by inducing a transformation between the exact and spontaneously broken phases of $\mathcal{N}=2$ Poincaré supersymmetry. We exploit the $K_4$ symmetry and its relation with the conformal symmetry to construct the dual Darboux transformations which generate spectrally shifted pairs of the rationally deformed AFF models. Two distinct pairs of intertwining operators originated from Darboux duality allow us to construct complete sets of the spectrum generating ladder operators that identify specific finite-gap structure of a deformed system and generate three distinct related versions of nonlinearly deformed $\mathfrak{sl}(2,{\mathbb R})$ algebra as its symmetry. We show that at half-integer $ν$, the Jordan states associated with confluent Darboux transformations enter the construction, and the spectrum of rationally deformed AFF systems undergoes structural changes.
We study topological T-duality for spaces with a semi-free $S^1-$action with isolated fixed points. Physically, these correspond to spacetimes containing Kaluza-Klein monopoles. We demonstrate that the physical dyonic coordinate of such spaces has an analogue in our formalism. By analogy with the Dirac monopole, we study these spaces as gerbes. We study the effect of Topological T-duality on these gerbes.
It is shown that the T-duality in σ-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher's duality transformation interchanges the topological and Noether charges.
A fundamental string with non-zero winding number can unwind in the presence of a Kaluza-Klein monopole. We use this fact to deduce the presence of a zero mode for the Kaluza-Klein monopole corresponding to excitations carrying H electric charge and we study the coupling of this zero mode to fundamental strings. We also a describe a T-dual process in which the momentum of a fundamental string ``unwinds'' in the presence of a H monopole. We use the coupling of string winding modes to the dyon collective coordinate of the Kaluza-Klein monopole to argue that there are stringy corrections to the K…
We study the duality relationship between M-theory and heterotic string theory at the classical level, emphasising the transformations between the Kaluza-Klein reductions of these two theories on the K3 and T^3 manifolds. Particular attention is devoted to the corresponding structures of sigma-model cosets and the correspondence between the p-brane charge lattices. We also present simple and detailed derivations of the global symmetries and coset structures of the toroidally-compactified heterotic theory in all dimensions D \ge 3, making use of the formalism of solvable Lie algebras.
It is shown that, with the only exception of $n=2$, the Einstein-Hilbert action in $n+D+d$ dimensions, with $n$ times, is invariant under the duality transformation $a\to \frac{1}{a}$ and $b\to \frac{1}{b}$, where $a$ is a Friedmann-Robertson-Walker scale factor in $D$ dimensions and $b$ a Brans-Dicke scalar field in $d$ dimensions respectively. We investigate the $2+D+d$ dimensional cosmological model in some detail.
We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve co…
The Kaluza-Klein monopole is a well known object in both gravity and string theory, related by T-duality to a "smeared" NS5-brane which retains the isometry around the duality circle. As the true NS5-brane solution is localized at a point on the circle, duality implies that the Kaluza-Klein monopole should show some corresponding behavior. In this paper, we express the Kaluza-Klein monopole as a gauged linear sigma model in two dimensions and show that worldsheet instantons give corrections to its geometry. These corrections can be understood as a localization in "winding space" which could be…
Extended Field Theories include Double Field Theory (DFT) and Exceptional Field Theory, which are respectively the T- and U-duality covariant formulations of the supergravity limit of String Theory and M-theory. Extended Field Theories do not live on spacetime, but on an extended spacetime, locally modelled on the space underlying the fundamental representation of the duality group. Despite its importance in M-theory, however, the global understanding of Extended Field Theories is still an open problem. In this thesis we propose a global geometric formulation of Extended Field Theory. Recall t…
S-duality of hetertotic / type II string theory compactified on a six dimensional torus requires the existence of Kaluza-Klein dyons, carrying winding charge. We identify the zero modes of the Kaluza-Klein monopole solution which are responsible for these dyonic excitations, and show that we get the correct degeneracy of dyons as predicted by S-duality. The self-dual harmonic two form on the Euclidean Taub-NUT space plays a crucial role in this construction.
We review the construction of the Kaluza-Klein monopole of the Type IIA theory in the most general case of a massive background, as well as its relation via T-duality with the Type IIB NS-5-brane. This last effective action is shown to be related by S-duality to the D5-brane effective action.
The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes. Replacing the fields by potentials and using instead a quadratic Klein-Gordon-type Lagrangian allows us to recover the double-Chern-Simons expression of conserved helicity and is shown to be equivalent to recently proposed alternative frameworks. Applied to the potential-modified theory the Dirac/Weyl-type approach yields again zero conserved charge, whereas the …
We give a simple proof of the known S-duality of Heterotic String theory compactified on a T^6. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a circle. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the circle is equal to the string length. We study the question of stability of the Heterotic NS5-brane with a transverse circle. For large radii the NS5-brane is absolutely stable. However for small radii it is only marginally stable. We also study the moduli space of 2 Kaluza-Klein monopoles and show that …
Using the SL(2,R)-duality in a dimensionally reduced spacetime in (the bosonic sector of) five-dimensional minimal supergravity, we construct general Kaluza-Klein black hole solutions which carry six independent charges, its mass, angular momentum along four dimensions, electric and magnetic charges of the Maxwell fields in addition to Kaluza-Klein electric and magnetic monopole charges.
We investigate possible existence of duality symmetries which exchange the Kaluza-Klein modes with the wrapping modes of a BPS saturated $p$-brane on a torus. Assuming the validity of the conjectured $U$-duality symmetries of type II and heterotic string theories and $M$-theory, we show that for a BPS saturated $p$-brane there is an SL(2,Z) symmetry that mixes the Kaluza-Klein modes on a $(p+1)$ dimensional torus $T^{(p+1)}$ with the wrapping modes of the $p$-brane on $T^{(p+1)}$. The field that transforms as a modular parameter under this SL(2,Z) transformation has as its real part the compon…
All regular four-dimensional black holes are constructed in the theory obtained by Kaluza-Klein reduction of five-dimensional Einstein gravity. They are interpreted in string theory as rotating bound states of D0- and D6-branes. Conservation of angular momentum is important for the stability of the bound states. The thermodynamics, the duality symmetries, and the near-horizon limit are explored.
Target space duality (T duality), which interchanges Kaluza--Klein and winding-mode excitations of the compactified heterotic string, is realized as a symmetry of a world-sheet action. Axion-dilaton duality (S duality), a conjectured nonperturbative SL(2,Z) symmetry of the same theory, plays an analogous role for five-branes. We describe a soliton spectrum possessing both duality symmetries and argue that the theory has an infinite number of dual string descriptions.
We present and study a new chain of 10-d T duality related solutions and their 11-d parents whose existence had been predicted in the literature based in U duality requirements in 4 d. The first link is the S dual of the D7-brane. The next link has 6 spatial worldvolume dimensions, it is charged w.r.t. the RR 7-form but depends only on 2 transverse dimensions since the third has to be compactified in a circle and is isometric and hence is similar in this respect to the KK monopole. The next link has 5 spatial worldvolume dimensions, it is charged w.r.t. the RR 6-form but depends only on 2 tran…
We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection, curvature as well as the Einstein equation are given in this parametrization. We also discuss the local duality between coordinates and quantum fields and the metric in this later reparametrization.
The dimensional reduction of (the bosonic sector of) five-dimensional minimal supergravity to four dimensions leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields (one of which has Chern-Simons coupling), whose field equations have SL(2,R)-invariance. Utilizing this SL(2,R)-duality, we provide a new formalism for solution generation. As an example, applying it to the Rasheed solution, which are known to describe dyonic rotating black holes (from the four-dimensional point of view) of five-dimensional pure gravity, we obtain rotating Kaluza-Klein bl…
Crosscap states and duality of Ising field theory in two dimensions
Faculty of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München（慕尼黑大学物理学院与阿诺德·索末菲理论物理中心）；School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology（华中科技大学物理学院与武汉国家强磁场科学中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Songshan Lake Materials Laboratory（松山湖材料实验室）
The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields and the dimensionally reduced equations of motion have SL(2,R)/SO(2)-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in whic…
It is shown that in 5D Kaluza-Klein theory there are everywhere regular wormhole-like solutions in which the magnetic field at the center is the origin of a rotation on the peripheral part of these solutions. The time on the peripheral part is topologically non-trivial and magnetic field is suppressed in comparison with the electric one.
The symmetry properties of the bosonic string effective action under Poisson-Lie duality transformations are investigated. A convenient and simple formulation of these duality transformations is found, that allows the reduction of the string effective action in a Kaluza-Klein framework. It is shown that the action is invariant provided that the two Lie algebras, forming the Drinfeld double, have traceless structure constants. Finally, a functional relation is found between the Weyl anomaly coefficients of the original and dual non-linear sigma models.
The system of D1 and D5 branes with a Kaluza-Klein momentum is re-investigated using the five-dimensional U-duality group E_{6(+6)}(Z). We show that the residual U-duality symmetry that keeps this D1-D5-KK system intact is generically given by a lift of the Weyl group of F_{4(+4)}, embedded as a finite subgroup in E_{6(+6)}(Z). We also show that the residual U-duality group is enhanced to F_{4(+4)}(Z) when all the three charges coincide. We then apply the analysis to the AdS(3)/CFT(2) correspondence, and discuss that among 28 marginal operators of CFT(2) which couple to massless scalars of AdS…
Open descendants with boundaries and crosscaps of non-trivial automorphism type are studied. We focus on the case where the bulk symmetry is broken to a Z_2 orbifold subalgebra. By requiring positivity and integrality for the open sector, we derive a unique crosscap of automorphism type g \in Z_2 and a corresponding g-twisted Klein bottle for a charge conjugation invariant. As a specific example, we use T-duality to construct the descendants of the true diagonal invariant with symmetry preserving crosscaps and boundaries.
We study how exotic branes, i.e. branes whose tensions are proportional to $g_s^{-α}$, with $α>2$, are realised in Exceptional Field Theory (EFT). The generalised torsion of the Weitzenböck connection of the $\operatorname{SL}(5)$ EFT which, in the language of gauged supergravity describes the embedding tensor, is shown to classify the exotic branes whose magnetic fluxes can fit into four internal dimensions. By analysing the weight diagrams of the corresponding representations of $\operatorname{SL}(5)$ we determine the U-duality orbits relating geometric and non-geometric fluxes. As a further…
We use the T-duality transformation which relates M-theory on T^3 to M-theory on a second T^3 with inverse volume to test the Banks-Fischler-Shenker-Susskind suggestion for the matrix model description of M-theory. We find evidence that T-duality is realized as S-duality for $U(\infty)$ N=4 Super-Yang-Mills in 3+1D. We argue that Kaluza Klein states of gravitons correspond to electric fluxes, wrapped membranes become magnetic fluxes and instantonic membranes are related to Yang-Mills instantons. The T-duality transformation of gravitons into wrapped membranes is interpreted as the duality betw…
The duality between the original Kaluza's theory and Klein's subsequent modification is duality between slicing and threading decomposition of the five-dimensional spacetime. The field equations of the original Kaluza's theory lead to the interpretation of the four-dimensional Lorentzian Kerr and Taub--NUT solutions as resulting from static electric and magnetic charges and dipoles in the presence of ghost matter and constant dilaton, which models Newton's constant.
We present the partition function of the refined Chern-Simons theory on $S^3$ with arbitrary A,B,C,D gauge algebra in terms of multiple sine functions. For B and C cases this representation is novel. It allows us to conjecture duality to some refined and orientifolded versions of the topological string on the resolved conifold, and carry out the detailed identification of different contributions. The free energies for D and C algebras possess the usual halved contribution from the A theory, i.e. orientable surfaces, and contributions of non-orientable surfaces with one cross-cup, with opposite…
Static, four-dimensional (4-d) black holes (BH's) in ($4+n$)-d Kaluza-Klein (KK) theory with Abelian isometry and diagonal internal metric have at most one electric ($Q$) and one magnetic ($P$) charges, which can either come from the same $U(1)$-gauge field (corresponding to BH's in effective 5-d KK theory) or from different ones (corresponding to BH's with $U(1)_M\times U(1)_E$ isometry of an effective 6-d KK theory). In the latter case, explicit non-extreme solutions have the global space-time of Schwarzschild BH's, finite temperature, and non-zero entropy. In the extreme (supersymmetric) li…
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…
In this Letter, based on the notion of gauge/gravity duality, we compute $ q $ SYK spectra in the presence of Yang-Baxter (YB) deformations. The gravitational counterpart of this duality turns out to be the YB deformed Almheiri-Polchinski (AP) model embodied with hyperbolic potential for the dilaton. Following Kaluza-Klein reduction on $ (AdS_2)_η\times (S^1/ Z_2) $, we compute the deformed Green's function that reproduces the original $ q $ SYK spectrum in the limit of vanishing deformations.
Kaluza-Klein gravity is revisted, with renewed interest, in a type IIB string theory on $S^1\times K3$. The irreducible curvature tensors are worked out in the, T-dual, emergent gravity in 4D to yield a non-linear U(1) gauge theory. Interestingly, the T-duality may be seen to describe an open/closed string duality at a self-dual string coupling. The obtained deformation in $AdS_5$ black hole is analyzed to introduce the notion of temperature in the emergent gravity underlying the recent idea of entropic force.
The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin
Asia Pacific Center for Theoretical Physics (APCTP), Postech（亚太理论物理中心（APCTP），浦项科技大学）；High Energy Physics Research Unit, Faculty of Science Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
We establish duality between real forms of the quantum deformation of the 4-dimensional orthogonal group studied by Fioresi et al. and the classification work made by Borowiec et al.. Classically these real forms are the isometry groups of $\mathbb{R}^4$ equipped with Euclidean, Kleinian or Lorentzian metric. A general deformation, named $q$-linked, of each of these spaces is then constructed, together with the coaction of the corresponding isometry group.
We discuss the condensation of charged tachyons in the heterotic theory on the Kaluza-Klein Melvin background. The arguments are based on duality relations which are expected to hold from the adiabatic argument. It is argued that in many cases the rank of the gauge group is not changed by the condensation, as opposed to naive expectations.
The Kaluza-Klein monopole has been recognized as a string background with significant non-geometric features: it must appear "localized" to winding strings to match the NS5-brane's localization on the T-dual circle. In this work, we explicitly construct this T-dual system in the doubled geometry formalism, which proves to successfully describe the duality despite a broken isometry on one side of the duality pair. We further suggest an extension of the doubled formalism to the gauged linear sigma models describing this system (both bosonic and supersymmetric) and show that previous calculations…
Different compactifications of six-dimensional string theory on $M_4 \times T^2$ are considered. Particular attention is given to the roles of the reduced modes as the $S$ and $T$ fields. It is shown that there is a discrete group of invariances of an equilateral triangle hidden in the model. This group is realized as the interchanges of the two-form fields present in the intermediate step of dimensional reduction in five dimensions. The key ingredient for the existence of this group is the presence of an additional $U(1)$ gauge field in five dimensions, arising as the dual of the Kalb-Ramond …
The low energy effective action describing the standard Kaluza-Klein reduction of heterotic string theory on a d-torus possesses a manifest O(d,d+16) symmetry. We consider generalized Scherk-Schwarz reductions of the heterotic string to construct massive gauged supergravities. We show that the resulting action can still be written in a manifestly O(d,d+16) invariant form, however, the U-duality transformations also act on the mass parameters. The latter play the dual role of defining the scalar potential and the nonabelian structure constants. We conjecture that just as for the standard reduct…
To clarify the mathematical structure of the RG-derived holographic dual field theory, we rewrite the string-theory based conventionally utilized dual holographic effective field theory based on the ADM decomposition of the metric tensor. This comparison leads us to claim that the RG-derived emergent holographic dual field theory takes into account higher-derivative curvature terms with gauge fixing in the string-theory based conventionally utilized Einstein-Klein-Gordon theory, giving rise to the RG flow of the metric tensor beyond the AdS (anti-de Sitter space) geometry. Furthermore, we comp…
We study the duality between string theory on AdS_3 X S^3 X S^3 and two-dimensional conformal theories with large N=4 superconformal algebra A_gamma. We discuss configurations of intersecting branes which give rise to such near-horizon geometries. We compute the Kaluza-Klein spectrum and propose that the boundary superconformal theory can be described by a sigma model on a suitable symmetric product space with a particular choice of anti-symmetric two-form.
The (4,0) supermultiplet in 6 dimensions contains a 4th rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32+32 supersymmetries. Dimensional reduction on a circle gives the 5D N=8 supergravity multiplet, with the 4th rank tensor reducing to the graviton. If there is an interacting (4,0) theory it should reduce to the full N=8 supergravity theory and so would give a conformal theory of gravity that would reduce to conventional gravity with the usual 2-derivative action at low energies. This paper revisits the conjecture that a non-lagrangian interacti…
The type IIA/IIB effective actions compactified on T^d are known to be invariant under the T-duality group SO(d, d; Z) although the invariance of the R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and Zumino,we introduce new potentials which are mixture of R-R potentials and the NS-NS 2-form in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant under the T-duality group. The argument is made in such a way…
