Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality (original) (raw)

S-duality for higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes

2014

We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus T n (n ≥ 2), by a noncommutative T n -deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, which is a purely noncommutative geometry phenomenon since the usual theory only has a Z 2 -symmetry. In particular, S-duality in this 6-dimensional higher abelian gauge theory model is shown to be, in this sense, on par with the usual 4-dimensional case. *

A Covariant Approach to Noncommutative M5-Branes

Progress of Theoretical Physics Supplement, 2007

We briefly review how to discuss noncommutative (NC) M5-branes and intersecting NC M5-branes from κ-invariance of an open supermembrane action with constant three-form fluxes. The κ-invariance gives rise to possible Dirichlet brane configurations. We shortly summarize a construction of projection operators for NC M5-branes and some intersecting configurations of NC M5-branes. A strong flux limit of them is also discussed.

Integrability of classical strings dual for noncommutative gauge theories

Journal of High Energy Physics, 2014

We derive the gravity duals of noncommutative gauge theories from the Yang-Baxter sigma model description of the AdS 5 ×S 5 superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4) abelian. Hence these should be called abelian Jordanian deformations. As a result, the gravity duals are shown to be integrable deformations of AdS 5 ×S 5. Then, abelian twists of AdS 5 are also investigated. These results provide a support for the gravity/CYBE correspondence proposed in arXiv:1404.1838.

D-branes, symplectomorphisms and noncommutative gauge theories

Nuclear Physics B - Proceedings Supplements, 2001

It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-form. A deformation of the Poisson bracket in terms of the Moyal brackets is then performed. A noncommutative gauge theory in terms of the Moyal star bracket is obtained. It is shown that all these theories may be described in terms of symplectic connections on symplectic fibrations. The world volume being its base manifold and the (sub)group of volume preserving diffeomorphisms generate the symplectomorphisms which preserve the (infinite dimensional) Poisson bracket of the fibration.

Effective actions of nongeometric five-branes

Physical Review D, 2014

An interesting consequence of string dualities is that they reveal situations where the geometry of a string background appears to be globally ill-defined, a phenomenon usually referred to as non-geometry. On the other hand, string theory contains extended objects with non-trivial monodromy around them, often dubbed defect or exotic branes in co-dimension two. We determine and examine the worldvolume actions and the couplings of certain such branes. In particular, based on specific chains of T and S-dualities, we derive the DBI and WZ actions, which describe the dynamics of type IIB fivebranes as well as their couplings to the appropriate gauge potentials associated to mixed symmetry tensors. Based on these actions we discuss how these branes act as sources of non-geometric fluxes. In one case this flux is what is usually termed Q flux, associated to a T-fold compactification, while in the S-dual case a type of non-geometry related to the Ramond-Ramond sector is encountered.

Marginal and relevant deformations of field theories and non-commutative moduli spaces of vacua

Nuclear Physics B, 2000

We study marginal and relevant supersymmetric deformations of the N = 4 super-Yang-Mills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F -term constraints. These field theories are dual to superstring theories propagating on deformations of the AdS 5 ×S 5 geometry. We study D-branes propagating in these vacua and introduce the appropriate notion of algebraic geometry for non-commutative spaces. The resulting moduli spaces of D-branes have several novel features. In particular, they may be interpreted as symmetric products of non-commutative spaces. We show how mirror symmetry between these deformed geometries and orbifold theories follows from T-duality. Many features of the dual closed string theory may be identified within the non-commutative algebra. In particular, we make progress towards understanding the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric tensor of the string is turned on, and we shed light on some aspects of discrete anomalies based on the non-commutative geometry.

A note on six-dimensional gauge theories

Physics Letters B, 1998

We study the new "gauge" theories in 5+1 dimensions, and their noncommutative generalizations. We argue that the θ-term and the non-commutative torus parameters appear on an equal footing in the non-critical string theories which define the gauge theories. The use of these theories as a Matrix description of M-theory on T 5 , as well as a closely related realization as 5-branes in type IIB string theory, proves useful in studying some of their properties. *

Noncommutative geometry and D-branes

Physics Letters B, 1997

We apply noncommutative geometry to a system of N parallel D-branes, which is interpreted as a quantum space. The Dirac operator defining the quantum differential calculus is identified to be the zero-momentum mode of the supercharge for strings connecting D-branes. As a result of the calculus, Connes' Yang-Mills action functional on the quantum space reproduces the dimensionally reduced U(N) super Yang-Mills action as the low energy effective action for D-brane dynamics. Several features that may look ad hoc in a noncommutative geometric construction are shown to have very natural physical or geometric origin in the D-brane picture in superstring theory.

Noncommutative Geometry from D0-branes in a Background B-field

1998

We study D0-branes in type IIA on T^2 with a background B-field turned on. We calculate explicitly how the background B-field modifies the D0-brane action. The effect of the B-field is to replace ordinary multiplication with a noncommutative product. This enables us to find the matrix model for M-theory on T^2 with a background 3-form potential along the torus and the lightlike circle. This matrix model is exactly the non-local 2+1 dim SYM theory on a dual T^2 proposed by Connes, Douglas and Schwarz. We calculate the radii and the gauge coupling for the SYM on the dual T^2 for all choices of longitudinal momentum and membrane wrapping number on the T^2.

Note on non-Abelian two-form gauge fields

Journal of High Energy Physics, 2012

Motivated by application to multiple M5-branes, we study some properties of non-Abelian two-form gauge theories. We emphasize that the fake curvature condition which is commonly used in the literature would restrict the dynamics to be either a free theory or a topological system. We then propose a modification of transformation law which simplifies the gauge transformation of 3-form field strength and enables us to write down a gauge invariant action. We then argue that a generalization of Stueckelberg mechanism naturally gives mass to the two-form gauge field. For the application to multiple M5-branes, it should be identified with the KK modes.