Wrapped M5-branes leading to five dimensional 2-branes

Abstract

We study the dimensional reduction of M5-branes wrapping special Lagrangian 3-cycles of a Calabi-Yau manifold and show explicitly that they result in 2-branes coupled to the hypermultiplets of ungauged N = 2 D = 5 supergravity theory. In addition to confirming previously known results, the calculation proves the relationship between them and provides further insight on how the topological properties of the compact space affect the lower dimensional fields.

BPS one-branes in five dimensions

“…Based on this observation, some hypermultiplet constructions in instanton and certain two-brane backgrounds were found and studied (last reference and [11,12]). More recently, we argued in [13] …”

“…Based on this observation, some hypermultiplet constructions in instanton and certain two-brane backgrounds were found and studied (last reference and [11,12]). More recently, we argued in [13] that the well known symplectic structure of quaternionic and special Kähler manifolds [14] can be used to construct hypermultiplet "solutions" based on covariance in symplectic space.…”

“…This is due to the fact that their underlying special Kähler geometry is very well understood (see for example [1,2,3,4,5,6,7,8] and references within). On the other hand, solutions in the hypermultiplets sector are rare, due in part to the mathematical complexity involved, since the hypermultiplets generally parameterize quaternionic manifolds [9].However, it was pointed out some years ago that due to the so-called c-map, the hypermultiplets in D = 5 for instance can be related to the much better understood D = 4 vector multiplets, and that the methods of special geometry, developed for the latter, can be applied to the former [10].Based on this observation, some hypermultiplet constructions in instanton and certain two-brane backgrounds were found and studied (last reference and [11,12]). More recently, we argued in [13] …”

Zero-branes and the symplectic hypermultiplets

“…However, it was pointed out some years ago that due to the so-called c-map, the hypermultiplets in D = 5 for instance can be related to the much better understood D = 4 vector multiplets, and that the methods of special geometry, developed for the latter, can be applied to the former [10]. Based on this observation, some hypermultiplet constructions in instanton and certain two-brane backgrounds were found and studied (last reference and [11,12]). Despite this, explicit calculations remain tedious even in the relatively simpler language of special geometry (as compared to the original quaternionic language).…”

Hyperbolic deformation of a gauge field theory and the hierarchy problem

“…By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in γ. Additionally the γ-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.It is well known that the physics of fields that arise from the dimensional reduction of M/string theory depends sensitively on the geometry and topology of the underlying space; in the context of Calabi-Yau compactification, the emerging theories contain supersymmetric multiplets and hypermultiplets, which can be described by defining a symplectic vectorial space where those fields appear as vectors and scalars; the inner product on such a space has the form of the modulus of splitcomplex numbers, rather than of the ordinary complex numbers [1,2,3,4,5]. The split-numbers can be generated by the substitution i → j, where j is a new complex unit with the property j 2 = 1; hence, one obtains an appropriate formulation for generating solutions and to gain understanding of the general structure of the theory, i.e.…”