A stringy model of pointlike particles

The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the gauge symmetry algebra generated by the C-bracket in double field theory (DFT). We show that the Vaisman algebroid is obtained by an analog of the Drinfel’d double of Lie algebroids. Based on a geometric realization of doubled space-time as a para-Hermitian manifold, we examine exterior algebras and a para-Dolbeault cohomology on DFT and discuss the structure of the Drinfel’d double behind the DFT gauge symmetry. Similar to the Courant algebroid in the generalized geometry, Lagrangian sub-bundles (L,L̃) in a para-Hermitian manifold play Dirac-like structures in the Vaisman algebroid. We find that an algebraic origin of the strong constraint in DFT is traced back to the compatibility condition needed for (L,L̃) to be a Lie bialgebroid. The analysis provides a foundation toward the “coquecigrue problem” for the gauge symmetry in DFT.

A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.

Perhaps the key untested idea in all of physics is that extra spatial dimensions might exist. Once we admit the possibility of extra dimensions several avenues for exploring theories of unification open up. Without extra dimensions there simply does not seem to be room for unification of the various forces. But where are these extra dimensions? For six decades after the pioneering work of Klein, the belief was that extra spatial dimensions — if they exist — are unobservable because they are tiny. The assumption was that any extra dimensions must be curled up on the Planck length scale of 10−35 meters. Eventually, that assumption began to be challenged. In 1983, for example, two physicists at Moscow’s Institute for Nuclear Research, Valery Rubakov and Misha Shaposhnikov, suggested there could be large extra dimensions that we have not yet observed. And in 1990, Ignatios Antoniadis, who was based at CERN, gave a serious proposal for how some of the extra dimensions of string theory could be 10−19 meters in length — still small, for sure, but much larger than previously thought. Such proposals were not without drawbacks, however, and in any case the ideas were not motivated by any deep underlying principles. Then came M-theory.

We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but not necessary. We then analyze compactifications of DFT on twisted double tori satisfying the consistency conditions. The effective theory is a Gauged DFT where the gaugings come from the duality twists. The action, bracket, global symmetries, gauge symmetries and their closure are computed by twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic string and lower dimensional gauged supergravities are particular examples of Gauged DFT.

Double field theory, twistors, and integrability in 4-manifolds

Grand unification at intermediate mass scales through extra dimensions

Double Field Theory (DFT) has emerged as a comprehensive framework for gravity, presenting a testable and robust alternative to General Relativity (GR), rooted in the $$\textbf{O}(D,D)$$ O ( D , D ) symmetry principle of string theory. These lecture notes aim to provide an accessible introduction to DFT, structured in a manner similar to traditional GR courses. Key topics include doubled-yet-gauged coordinates, Riemannian versus non-Riemannian parametrisations of fundamental fields, covariant derivatives, curvatures, and the $$\textbf{O}(D,D)$$ O ( D , D ) -symmetric augmentation of the Einstein field equation, identified as the unified field equation for the closed string massless sector. By offering a novel perspective, DFT addresses unresolved questions in GR and enables the exploration of diverse physical phenomena, paving the way for significant future research.

The Double Field Theory (DFT) is formulated on a certain class of a metric algebroid, where the structure functions satisfy the pre-Bianchi identity. The derived bracket formulation of the metric algebroid by the Dirac generating operator is applied. The action is formulated by a projected generalized Lichnerowicz formula which is a generalization of the analogous formulation in gravity and supergravity. The flux of the dilaton in this setting is introduced via an ambiguity in the Dirac generating operator, while the dilaton is introduced via an ambiguity of the divergence on the metric algebroid. This talk is based on [1].

Previous constructions of supersymmetry for double field theory have relied on the so-called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk–Schwarz reduction is imposed. The equivalence between the generalised Scherk–Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a biproduct we write the generalised Killing spinor equations for the supersymmetric double field theory.

Solving the hierarchy problem without supersymmetry or extra dimensions: an alternative approach

This thesis is mainly devoted to studying integrable deformations of the ${\rm AdS}_5 \times {\rm S}^5$ superstring and generalized supergravity. We start to give a brief review of the ${\rm AdS}_5 \times {\rm S}^5$ superstring formulated in the Green-Schwartz formalism, and then introduce homogeneous Yang-Baxter (YB) deformation of the ${\rm AdS}_5 \times {\rm S}^5$ superstring based on $r$-matrices which are solutions to the homogeneous classical YB equation. By performing a supercoset construction, we derive the general formula for homogeneous YB deformed backgrounds associated with bosonic $r$-matrices. The deformed backgrounds are shown to be solutions of the standard type IIB supergravity or generalized supergravity. Next, we explain that homogeneous YB deformation can be regarded as a kind of the $O(d,d)$ duality transformations. Once YB deformations are realized as duality transformations, the corresponding $O(d,d)$ transformations are applied to almost all backgrounds. Moreover, we discuss spacetime structures of homogeneous YB deformed backgrounds and clarify a T-fold structure of them by showing the associated $O(d,d; \mathbb{Z})$ $T$-duality monodromy. Finally, we consider the Weyl invariance of string theories in generalized supergravity backgrounds. We show that generalized supergravity can be reproduced from double field theory with the dilaton depending on a linear dual coordinate. From this result, we construct a possible counterterm to cancel out the Weyl anomaly of bosonic string theories on generalized supergravity backgrounds. In particular, we show that the counterterm is definitely local. In this sense, string theories can be consistently defined in generalized supergravity backgrounds.

New instability for rotating black branes and strings

Recently proposed exceptional field theories (EFTs) making manifest the duality En(n) symmetry, first observed as nonlinearly realized symmetries of the maximal d=3,4,...,9 supergravity (n=11−d) and containing 11D and type IIB supergravity as sectors, were formulated in enlarged spacetimes. In the case of E7(7) EFT such an enlarged spacetime can be identified with the bosonic body of the d=4 central charge superspace Σ(60|32), the N=8d=4 superspace completed by 56 additional bosonic coordinates associated to central charges of the maximal d=4 supersymmetry algebra.In this paper we show how the hypothesis on the relation of all the known En(n) EFTs, including n=8, with supersymmetry leads to the conjecture on existence of 11D exceptional field theory living in 11D tensorial central charge superspace Σ(528|32) and underlying all the En(n) EFTs with n=2,...,8, and probably the double field theory (DFT). We conjecture the possible form of the section conditions of such an 11D EFT and show that quite generic solutions of these can be generated by superparticle models the ground states of which preserve from one half to all but one supersymmetry. The properties of these superparticle models are briefly discussed. We argue that, upon quantization, their quantum states should describe free massless non-conformal higher spin fields in D=11. We also discuss some relevant representations of the M-theory superalgebra which, in the present context, describes supersymmetry of the 11D EFT.

Recently, a method for calculating the quantum spectrum of black holes has been proposed. We show that this method can be applied for radiations of 4 + n - dimensional water around a DNA. In this model, DNA acts like a black hole and produces a curved space-time in a water around it. In these conditions, molecules of water in four dimensional universe are entangled with some DNA-like structures in extra dimension. Consequently, the effects of structures of water in extra dimensions can be observed in four dimensions. The entangled structures emit some quantum spectrum which can be transmitted to pure waters. These waves produce a curved space-time in pure water and make an entanglement between structure of water on four and DNA-like structures in extra dimensions. As a result, some signatures of DNAs can be observed in pure water. This model helps us to understand the reason for the emergence of life on the earth. To explain the model better, we unify Darwin’s theory with string theory in a new Darwinian’s string theory. In this theory, a zero dimensional manifold decays into two types of closed strings. One type decays into open strings and then these strings join to each other and form cosmos. Another type decays into open strings which form biological matters like DNAs and molecules of water in universe and anti-DNAs and anti-water in anti-universe. Thus, DNAs and molecules water are connected to each other and anti-DNAs and molecules of anti-water in anti-universe through some closed strings. These strings helps to molecules of water to store their informations in extra dimension and have long time memory. Because, information that are transformed into extra dimensions through closed strings, could be returned into universe. Also, these closed strings could have the main role in DNA transduction. Because, they connect two tubes one including water and DNA and another pure water in universe to two tubes including anti-DNA and water in anti-universe and transform properties of DNA into pure water. As a result, Darwinian string theory can confirm both water memory and DNA transduction. Finally, this theory response to this question that why memory of water couldnt remain for a long time. In this model, open strings which connects atoms in universe with anti-atoms in anti-universe interact with open strings which connects molecules of water and anti-water and decrease their entanglement. This causes that exchanging information between water and anti-water decreases and memory is dis-appeared.

Local discrete symmetry in the brane neighborhood