High Energy Physics Theory

String geometry theory is a candidate of the non-perturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how superstring backgrounds are described in string geometry theory. In this paper, we show that all the type IIA, IIB, SO(32) type I, and SO(32) andE8?E8heterotic superstring backgrounds are embedded in configurations of the fields of a single string geometry model. Especially, we show that the configurations satisfy the equations of motion of the string geometry model inα????if and only if the embedded string backgrounds satisfy the equations of motion of the supergravities, respectively. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.

We find a large class of supersymmetric domain wall solutions from six-dimensionalN=(2,2)gauged supergravity with various gauge groups. In general, the embedding tensor lives in144crepresentation of the global symmetrySO(5,5). We explicitly construct the embedding tensors in15??and40¯¯¯¯¯¯??representations ofGL(5)??R+?SL(5)?�SO(5,5)leading toCSO(p,q,5?�p?�q)andCSO(p,q,4?�p?�q)??R4sgauge groups, respectively. These gaugings can be obtained fromS1reductions of seven-dimensional gauged supergravity withCSO(p,q,5?�p?�q)andCSO(p,q,4?�p?�q)gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in15??or40¯¯¯¯¯¯??representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both15??and40¯¯¯¯¯¯??representations, the domain walls turn out to be14-supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang-Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensionalN=4gauged supergravity.

The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub `domestic geometry', the generalization of special Kähler geometry which does not require the underlying manifold to be Kähler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kähler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such `Ooguri-Vafa' manifolds, including their Liouville properties.Our second goal is to present some novel speculation on the extension of the swampland program to no-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case.

We show that theories of massless Kähler-Dirac fermions suffer from an anomaly which is topological in origin and breaks aU(1)symmetry, unique to Kähler-Dirac theories, down to a discrete subgroup depending on the Euler number of the background space and the number of flavors. Furthermore, in the presence of interactions, cancellation of this anomaly places constraints on the number of massless fermions. We write down Yukawa interactions respecting this discrete symmetry which we argue are capable of generating fermion masses without breaking symmetries and, if carefully chosen, can yield chiral low energy theories. We show that the simplest example of such a model exhibits aSpin(7)?Spin(4)flavor symmetry. If theSpin(7)symmetry is subsequently Higgsed toSpin(6)the resultant low energy theory possesses the symmetries and fermion representations of the Pati-Salam model.

We find that spinning particles with suitable couplings propagating in certain supersymmetric backgrounds ofD=4,N=2andD=5,N=1minimal supergravities are invariant under symmetries generated by the twisted covariant form hierarchies of these theories. We also compare our results with the symmetries of spinning particles generated by Killing-Yano forms which are responsible for the separability properties of some gravitational backgrounds.

We resolve the subregion bulk reconstruction paradox posed by Alhmeiri et al for the case of AdS/Rindler wedges without invoking error correction. The resolution comes from the observation that as bulk isometries map act as conformal symmetries in the boundary, the action of an isometric change of coordinate charts on the bulk field is represented on the boundary representation of the field by a unitary map. This is the unitary map which implements the corresponding conformal transformation. The different AdS/Rindler regions being isometric, the corresponding subregion representations are thus related to each other by this unitary map. In this paper we prove this transformation law and show that it immediately resolves the paradox.

We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by aP??-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by anL??-algebra which is not aP??-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define aP??-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based onA??-algebras.

The light-cone gauge approach toTT¯¯¯¯deformed models is used to derive theTT¯¯¯¯deformed matrix nonlinear Schrödinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of theTT¯¯¯¯deformed nonlinear Schrödinger and Korteweg--de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under theTT¯¯¯¯deformation. However, whether the soliton's size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. TheTT¯¯¯¯deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.

Cosmological models of the early or late universe exhibit (quasi) de Sitter space-times with different stability properties. Considering models derived from string theory, the swampland program does not provide for now a definite characterisation of this stability. In this work we focus on de Sitter solutions of 10d type II supergravities, candidates for classical de Sitter string backgrounds: surprisingly, all known examples are unstable withηV<??. We aim at proving the existence of such a systematic tachyon, and getting formally a bound on the value ofηV. To that end, we develop three methods, giving us various sufficient conditions for having a tachyon upon assumptions, in analogy with de Sitter no-go theorems. Our analysis eventually indicates the existence of variety of different tachyons, and related bounds onηV. We use this knowledge to find 10 new de Sitter solutions of type IIB supergravity, that have tachyons of a different kind, higherηVvalues and new 6d geometries. One solution even appears to be stable, with however non-compact extra dimensions.

Using holographic idea, we study the entanglement of purification in a field theory with a critical point in intermediate and low temperature regime. This theory includes temperatureTas well as chemical potentialμ. In the intermediate regime, due to chemical potential, we observe that new terms proportional to temperature square appear in the final result of entanglement of purification or equivalently, apart fromT0andT4terms in the case ofμ=0, it contains the terms proportional toT2. Our results also indicate that the entanglement of purification, i.e. the correlation between subsystems, can decrease or increase depending on the value ofμTwhen the other parameters are kept fixed. However, in the low temperature limit, the correlation always decreases, comparing to theμ=0case, independent of the value ofμTwhen the other parameters do not alter. The existence of a critical point in the theory changes the behavior of entanglement of purification in such a way that the entanglement of purification experiences a maximum or minimum. Moreover, near the critical point, we analytically show that the critical exponent is equal to 0.5 in both regimes and also the term proportional toT2changes sign and becomes negative in the intermediate regime.