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Arjan Keurentjes

Publications and source records attributed to Arjan Keurentjes.

At least 19 recordsLinked to original sources
arXiv2006

Determining the dual

We study the R -> 0 limit for heterotic strings of either kind (Spin(32)/Z_2 or E_8 x E_8) compactified on a circle, in the presence of an arbitrary Wilson line. Though for generic Wilson line this limit leads to chaotic behaviour, there are two distinguished, countable subsets of Wilson lines, that are dense in the total space of Wilson lines: One subset leads to decompactification limits; a second subset converges onto periodic orbits. Many of the implications carry over to heterotic strings on a circle of small but finite radius. To complete the picture, we discuss global aspects of the moduli-space, compare it with the ``fiducial'' moduli-space for type I strings on a circle, give a derivation of the map between the moduli of the two heterotic string theories on a circle at an arbitrary point in the moduli space, and compute the smallest radius that can be probed.

hep-th↗
arXiv2005

Poincare Duality and G+++ algebra's

Theories with General Relativity as a sub-sector exhibit enhanced symmetries upon dimensional reduction, which is suggestive of ``exotic dualities''. Upon inclusion of time-like directions in the reductions one can dualize to theories in different space-time signatures. We clarify the nature of these dualities and show that they are well captured by the properties of infinite-dimensional symmetry algebra's (G+++ algebra's), but only after taking into account that the realization of Poincare duality leads to restrictions on the denominator subalgebra appearing in the non-linear realization. The correct realization of Poincare duality can be encoded in a simple algebraic constraint, that is invariant under the Weyl-group of the G+++ algebra, and therefore independent of the detailed realization of the theory under consideration. We also construct other Weyl-invariant quantities that can be used to extract information from the G+++ algebra without fixing a level decomposition.

hep-th↗
arXiv2004

Time-like T-duality algebra

When compactifying M- or type II string-theories on tori of indefinite space-time signature, their low energy theories involve sigma models on E_{n(n)}/H_n, where H_n is a not necessarily compact subgroup of E_{n(n)} whose complexification is identical to the complexification of the maximal compact subgroup of E_{n(n)}. We discuss how to compute the group H_n. For finite dimensional E_{n(n)}, a formula derived from the theory of real forms of E_n algebra's gives the possible groups immediately. A few groups that have not appeared in the literature are found. For n=9,10,11 we compute and describe the relevant real forms of E_n and H_n. A given H_n can correspond to multiple signatures for the compact torus. We compute the groups H_n for all compactifications of M-, M*-, and M'-theories, and type II-, II*- and II'-theories on tori of arbitrary signature, and collect them in tables that outline the dualities between them. In an appendix we list cosets G/H, with G split and H a subgroup of G, that are relevant to timelike toroidal compactifications and oxidation of theories with enhanced symmetries.

hep-th↗
arXiv2004

E_11: Sign of the times

We discuss the signature of space-time in the context of the E_11 -conjecture. In this setting, the space-time signature depends on the choice of basis for the ``gravitational sub-algebra'' A_10, and Weyl transformations connect interpretations with different signatures of space-time. Also the sign of the 4-form gauge field term in the Lagrangian enters as an adjustable sign in a generalized signature. Within E_11, the combination of space-time signature (1,10) with conventional sign for the 4-form term, appropriate to M-theory, can be transformed to the signatures (2,9) and (5,6) of Hull's M*- and M'-theories (as well as (6,5), (9,2) and (10,1)). Theories with other signatures organize in orbits disconnected from these theories. We argue that when taking E_11 seriously as a symmetry algebra, one cannot discard theories with multiple time-directions as unphysical. We also briefly explore links with the SL(32,R) conjecture.

hep-th↗
arXiv2003

U-duality (sub-)groups and their topology

We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional coset sigma model can be interpreted as a dimensional reduction of a higher dimensional theory. Similar criteria exist for higher dimensional sigma models, though less decisive. Careful examination of the topology of symmetry groups rules out certain proposals for M-theory symmetries, which are not ruled out at the level of the algebra's. We conclude with an observation on the relation between the ``generalized holonomy'' proposal, and the actual symmetry groups resulting from E_10 and E_11 conjectures.

hep-th↗
arXiv2003

The topology of U-duality (sub-)groups

We discuss the topology of the symmetry groups appearing in compactified (super-)gravity, and discuss two applications. First, we demonstrate that for 3 dimensional sigma models on a symmetric space G/H with G non-compact and H the maximal compact subgroup of G, the possibility of oxidation to a higher dimensional theory can immediately be deduced from the topology of H. Second, by comparing the actual symmetry groups appearing in maximal supergravities with the subgroups of SL(32,R) and Spin(32), we argue that these groups cannot serve as a local symmetry group for M-theory in a formulation of de Wit-Nicolai type.

hep-th↗
arXiv2003

Triples, Fluxes, and Strings

We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactifications on smooth spaces. The last class of vacua considered are compactifications on singular spaces with non-trivial discrete fluxes. We find a number of new components in the string moduli space. Contained in some of these components are M theory compactifications with novel kinds of ``frozen'' singularities. We are naturally led to conjecture the existence of new dualities relating spaces with different singular geometries and fluxes. As our study of these vacua unfolds, we also learn about additional topics including: F theory on spaces without section, automorphisms of del Pezzo surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we comment on how the data we gain about the M theory three-form might be interpreted.

hep-th↗
arXiv2003

The group theory of oxidation II: Cosets of non-split groups

The oxidation program of hep-th/0210178 is extended to cover oxidation of 3-d sigma model theories on a coset G/H, with G non-compact (but not necessarily split), and H the maximal compact subgroup. We recover the matter content, the equations of motion and Bianchi identities from group lattice and Cartan involution. Satake diagrams provide an elegant tool for the computations, the maximal oxidation dimension, and group disintegration chains can be directly read off. We give a complete list of theories that can be recovered from oxidation of a 3 dimensional coset sigma model on G/H, where G is a simple non-compact group.

hep-th↗
arXiv2003

The group theory of oxidation

Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic sector of 3 dimensional maximal supergravity. The reverse process, oxidation, is the reconstruction of a higher dimensional gravity theory from a coset sigma model. Using the group G as starting point, the higher dimensional models follow essentially from decomposition into subgroups. All equations of motion and Bianchi identities can be directly reconstructed from the group lattice, Kaluza-Klein modifications and Chern-Simons terms are encoded in the group structure. Manipulations of extended Dynkin diagrams encode matter content, and (string) dualities. The reflection symmetry of the ``magic triangle'' for E_n gravities, and approximate reflection symmetry of the older ``magic triangle'' of supergravities in 4 dimensions, are easily understood in this framework.

hep-th↗
arXiv2002

Oxidation = group theory

Dimensional reduction of theories involving (super-)gravity gives rise to sigma models on coset spaces of the form G/H, with G a non-compact group, and H its maximal compact subgroup. The reverse process, called oxidation, is the reconstruction of the possible higher dimensional theories, given the lower dimensional theory. In 3 dimensions, all degrees of freedom can be dualized to scalars. Given the group G for a 3 dimensional sigma model on the coset G/H, we demonstrate an efficient method for recovering the higher dimensional theories, essentially by decomposition into subgroups. The equations of motion, Bianchi identities, Kaluza-Klein modifications and Chern-Simons terms are easily extracted from the root lattice of the group G. We briefly discuss some aspects of oxidation from the E_{8(8)}/SO(16) coset, and demonstrate that our formalism reproduces the Chern-Simons term of 11-d supergravity, knows about the T-duality of IIA and IIB theory, and easily deals with self-dual tensors, like the 5-tensor of IIB supergravity.

hep-th↗
arXiv2002

Twisting E8 Five-Branes

We consider the tensor theory on coincident E8 5-branes compactified on a three torus. Using string theory, we predict that there must be distinct components in the moduli space of this theory.We argue that new superconformal field theories are to be found in these sectors with, for example, global G2 and F4 symmetries. In some cases, twisted E8 5-branes can be identified with small instantons in non-simply-laced gauge groups. This allows us to determine the Higgs branch for the fixed point theory. We determine the Coulomb branch by using an M theory dual description involving partially frozen singularities. Along the way, we show that a D0-brane binds to two D4-branes, but not to an Sp-type O4-plane (despite the existence of a Higgs branch). These results are used to check various string/string dualities for which, in one case (quadruple versus NVS), we present a new argument. Finally, we describe the construction of new non-BPS branes as domain walls in various heterotic/type I string theories.

hep-th↗
arXiv2002

Flat connections from flat gerbes

We discuss some aspects of heterotic-Type I duality. We focus on toroidal compactification, with special attention for the topology of the gauge group, and the topology of the bundle. We review the arguments leading to a classification of Spin(32)/Z_2-bundles over tori, suitable for string compactifications. A central role is played by n-gerbes with connection, a generalization of bundles with connection.

hep-th↗
arXiv2001

Classifying orientifolds by flat n-gerbes

The discrete tensorial charges carried by orientifold planes define n-gerbes in space-time. The simplest way to ensure a consistent string compactification is to require these gerbes to be flat. This results in expressions for the local gerbe-holonomies around each orientifold plane, describing its charges. Inverting the procedure and considering all flat gerbes leads to a classification of orientifold configurations. Requiring that the tadpole is cancelled by adding D-branes, we classify all supersymmetric orientifolds on T^k/Z_2 with 2^k O(9-k) planes at the fixed points, for k less or equal to 6. For k=6 these theories organize in orbits of the SL(2,Z) S-duality symmetry of N=4 supersymmetric gauge theories.

hep-th↗
arXiv2001

Discrete moduli for Type I compactifications

We study type I compactification on a 4-torus, with a non-trivial discrete background RR 4-form field. By using string dualities and recent insights for gauge theories on tori, we find that a non-trivial background for the RR 4-form is correlated with Spin(32)/Z_2 bundles that are described by a ``non-trivial quadruple'' of holonomies. We also briefly discuss other discrete moduli for the type I string, and variants of orientifold planes.

hep-th↗
arXiv2000

New vacua for Yang-Mills theory on a 3-torus

In this thesis we discuss recent new insights in the structure of the moduli space of flat connections of Yang-Mills theory on a 3-torus. Chapter 2 discusses the computation of Witten's index for 4-dimensional gauge theories, and the paradox that arises in comparing various computations. This was resolved by the discovery that for orthogonal and exceptional gauge groups, periodic flat connections exist that are contained in seperate, disconnected components of the moduli space. Chapter 3 and 4 discuss some aspects of the construction of holonomies parametrising vacua on such disconnected components. Chapter 5 demonstrates a construction of vacua and holonomies for gauge theories with classical groups, with non-periodic (twisted) boundary conditions, using an orientifold description. The new solutions with exceptional and orthogonal gauge groups also occur in string theory. Chapter 6, containing previously unpublished material, shows that they can be realised within heterotic string theories as asymmetric orbifolds. The presence of string winding states modifies the analysis for the gauge theory in a crucial way, eliminating many possibilities. The remaining ones are related by string dualities to known and new theories.

hep-th↗
arXiv2000

Orientifolds and twisted boundary conditions

It is argued that the T-dual of a crosscap is a combination of an O+ and an O- orientifold plane. Various theories with crosscaps and D-branes are interpreted as gauge-theories on tori obeying twisted boundary conditions. Their duals live on orientifolds where the various orientifold planes are of different types. We derive how to read off the holonomies from the positions of D-branes in the orientifold background. As an application we reconstruct some results from a paper by Borel, Friedman and Morgan for gauge theories with classical groups, compactified on a 2-- or 3--torus with twisted boundary conditions.

hep-th↗
arXiv1999

Flat connections for Yang-Mills theories on the 3--torus

We discuss the moduli space of flat connections of Yang-Mills theories formulated on T^3 x R, with periodic boundary conditions. When the gauge group is SO(N>=7), G_2, F_4, E_6, E_7 or E_8, the moduli space consists of more than one component.

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