Citation Context

...ses arguing for noncommutativity of string coordinates in the presence of a B-field, in a Hamiltonian treatment [13] and also in a worldsheet treatment that makes the computations particularly simple =-=[14]-=-. In the latter paper, it was suggested that rather classical features of the propagation of strings in a constant magnetic field [41,42] can be reinterpreted in terms of noncommutativity of spacetime...

Citation Context

... our first analogy to string theory. Consider the string σ-model that was described in section 1.3. The open string propagator on the boundary of a disk Σ in a constant background B field is given by =-=[31, 33, 41]-=- where � x i (t) x j (t ′ ) � = −α ′ G ij ln(t − t ′ ) 2 + i 2 θij sgn(t − t ′ ) , (3.10) θ ij = −(2πα ′ ) 2 � 1 g + 2πα ′ B B 1 g − 2πα ′ �ij B 19 , (3.11)sand Gij = gij − (2πα ′ � 2 ) Bg −1 B � ij (...

Citation Context

...θ . A rather similar argument shows that world-volumes of D-branes in the Wess-Zumino-Witten model are described by field theory on “fuzzy spheres” as described in Sec. VI.B (Alekseev, Recknagel, and =-=Schomerus 1999-=-). An interesting difference is that here dB ̸= 0 and the corresponding algebra is not associative, except in suitable limits. 2. Deformation quantization from topological open string theory The idea ...

Citation Context

...ding to eqs.(2.16), (2.17) in the static gauge. 7 Of course the antisymmetric part of constant background ˜ G µν has the effect of making the ordinary products in (3.2) into non-commutative ∗ products=-=[24, 25, 26, 23]-=-. This can be reexpressed in terms of ordinary products by including terms with higher derivatives. In the present case these extra terms vanish due to symmetry reasons. 113.2 Fermionic zero modes on...

Citation Context

...infinite collection of D0branes can make higher Dp-branes [1,2,3]. This motivated the discovery of noncommutative geometry in string theory [4,5], which was later studied by various authors including =-=[6,7]-=-. More recently, following the work of Sen [8] the phenomenon of tachyon condensation on D-branes was studied by various people including [9-16]. In particular, it became clear that by turning on a B ...

Citation Context

...orus. Even though this initial observation was re-considered and generalized by many authors [2{4], all the subsequent work is restricted tosat backgrounds. A perturbative analysis along the lines of =-=[4]-=-, on the other hand, shows that the quantization of world-volume geometries should be a much more general phenomenon which persists in the case of curved backgrounds. In this work we shall present the...

Citation Context

...nish generically after summing over all permutations of the insertion points at the boundary of the world-sheet. But we learn from the relation between open string theory and non-commutative geometry =-=[27, 28, 29, 30]-=- that the products of boundary operators in a conformal field theory (such as the Gepner models) can depend very much on the order in which fields are multiplied. Only a small number of fields, namely...

Citation Context

...roduction Noncommutative gauge theories have attracted much interest recently. They appear naturally in various decoupling limits of the worldvolume theories of D-branes in a background NS-NS B-field =-=[1, 2, 3, 4, 5, 6]-=- and provide simplified settings for studying nonlocal effects in string theory. In noncommutative gauge theories, gauge invariance becomes subtle. When there is only adjoint matter, translations alon...