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A<sc>bstract</sc> In this paper we present a large class of flux backgrounds and solve the shortest vector problem in type IIB string theory on an orientifold of the 1⁹Landau-Ginzburg model. 

A<sc>bstract</sc> We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and find it can be expressed as a product of holomorphic Ray-Singer torsions. We discuss its topological properties and potential gauge and gravitational anomalies. We show these anomalies can be cancelled using Green-Schwarz-like counter-terms. We also discuss the dependence on the background geometry, and in particular the choice of hermitian metric needed for quantisation. Given suitable topological constraints, this dependence may again be cancelled by the addition of purely background-dependent counter-terms. We also explain how our methods provide the one-loop partition functions of a large class of more general holomorphic field theories in terms of holomorphic Ray-Singer torsions. 

A<sc>bstract</sc> An extended search for anomaly free matter coupledN= (1,0) supergravity in six dimension is carried out by two different methods which we refer to as the graphical and rank methods. In the graphical method the anomaly free models are built from single gauge group models, called nodes, which can only have gravitational anomalies. We search for anomaly free theories with gauge groupsG₁× … ×G_nwithn= 1,2,… (any number of factors) andG₁× … ×G_n×U(1)_Rwheren= 1,2,3 andU(1)_Ris theR-symmetry group. While we primarily consider models with the tensor multiplet numbern_T= 1, we also provide some results forn_T≠ 1 with an unconstrained number of charged hypermultiplets. We find a large number of ungauged anomaly free theories. However, in the case ofR-symmetry gauged models withn_T= 1, in addition to the three known anomaly free theories withG₁×G₂×U(1)_Rtype symmetry, we find only six new remarkably anomaly free models with symmetry groups of the formG₁×G₂×G₃×U(1)_R. In the case ofn_T= 1 and ungauged models, excluding low rank group factors and considering only low lying representations, we find all anomaly free theories. Remarkably, the number of group factors does not exceed four in this class. The proof of completeness in this case relies on a bound which we establish for a parameter characterizing the difference between the number of non-singlet hypermultiplets and the dimension of the gauge group. 

A bstract We construct the four-derivative supersymmetric extension of (1, 0), 6 D supergravity coupled to Yang-Mills and hypermultiplets. The hypermultiplet scalars are taken to parametrize the quaternionic projective space Hp ( n ) = Sp( n , 1)/Sp( n ) × Sp(1) R . The hyperscalar kinetic term is not deformed, and the quaternionic Kähler structure and symmetries of Hp ( n ) are preserved. The result is a three parameter Lagrangian supersymmetric up to first order in these parameters. Considering the case of Hp (1) we compare our result with that obtained from the compactification of 10 D heterotic supergravity on four-torus, consistently truncated to N = (1, 0), in which the hyperscalars parametrize SO(1, 4)/SO(4). We find that depending on how the Sp(1) is embedded in the SO(4), the results agree for a specific value of the parameter that governs the higher derivative hypermultiplet couplings. 

A bstract We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived. 

A bstract Type IIB flux vacua based on Landau-Ginzburg models without Kähler deformations provide fully-controlled insights into the non-geometric and strongly-coupled string landscape. We show here that supersymmetric flux configurations at the Fermat point of the 1 9 model, which were found long-time ago to saturate the orientifold tadpole, leave a number of massless fields, which however are not all flat directions of the superpotential at higher order. More generally, the rank of the Hessian of the superpotential is compatible with a suitably formulated tadpole conjecture for all fluxes that we found. Moreover, we describe new infinite families of supersymmetric 4d $$ \mathcal{N} $$ N = 1 Minkowski and AdS vacua and confront them with several other swampland conjectures. 

A bstract Higher derivative couplings of hypermultiplets to 6 D, N = (1 , 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α ′ higher derivative corrections. Reduction on T 4 is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset SO(4 , 4) / (SO(4) × SO(4)). While the SO(4 , 4) symmetry is ensured by Sen’s construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the SO(4) × SO(4) down to its SO(4) diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction. 

A bstract We derive the component structure of 11D, N = 1/8 supergravity linearized around eleven-dimensional Minkowski space. This theory represents 4 local supersymmetries closing onto 4 of the 11 spacetime translations without the use of equations of motion. It may be interpreted as adding 201 auxiliary bosons and 56 auxiliary fermions to the physical supergravity multiplet for a total of 376 + 376 components. These components and their transformations are organized into representations of SL(2; C ) × G 2 .