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...e classical tachyon potential on a D-p brane of the bosonic string theory has a stationary point where the total negative potential energy due to the tachyon exactly cancels the tension of the D-brane=-=[1, 2]-=-. At this stationary point the configuration is indistinguishible from the vacuum where there is no brane. A similar argument can be given for the tachyon potential on a D-brane anti-D-brane system or...

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...the total negative potential energy exactly cancels the tension of the D–brane [1]. Moreover, solitonic lump solutions of the tachyon effective potentials are identified with lower–dimensional branes =-=[2, 1]-=-. Similar conjectures exist for the tachyon living on a coincident D-brane anti-D-brane pair, or on non-BPS D-branes of type IIA or IIB superstring theories [3, 4, 5, 6, 7, 8]. String field theory has...

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... additive constant in V (T) such that it vanishes at T = 0. Thus the total energy of the D-brane for a given value of T will be given by M + V (T) = M{1 + f(T)} . (1.2) According to the conjecture of =-=[11, 12]-=-, at some extremum T0 of the tachyon potential the negative contribution of the tachyon potential exactly cancels the mass of the D-brane. Thus according to this conjecture 1 + f(T0) = 0 . (1.3) Altho...

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...he ‘generators’ of the world-volume algebra appear on equal footing, it should be possible to develop a rather general approach towards effective theories on non-commutative spaces. The techniques of =-=[19]-=- provide another step in this direction. It was shown there that non-commutativity of the boundary operator product expansion is the only obstruction in boundary deformation theory. In this sense, a d...

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...ured that, instead of spatially homogeneous tachyon condensation, solitonic lump configurations where the tachyon field asymptotically approaches the vacuum value represent lower dimensional D-branes =-=[2, 3]-=-. Though there are no tachyonic modes on a BPS D-brane of Type II superstring theory, by considering the unstable systems, such as a non-BPS D-brane or a coincident D-brane anti-D-brane pair, tachyoni...

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...ons of these moduli fields ∆a (see figure 4). In this case one has to sum over all these contributions inducing a consistent open string moduli dependence of the superpotential couplings. As shown in =-=[39]-=-, these integrable boundary deformations lead to the expected exponential dependence. Φ Φ x 1,x2 X a,x1 X XΦ X X X x n−1,xn Dx 1 Dx n X Φx n ,b ∆ a ∆ a Da Φab X ∆ Db b ∆b Da Db Λa E2 Λ b Λ a E2 Λ b Fi...

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...n worldvolume non-commutativity as introduced in [1] and non-commuting moduli as discovered by Witten [43]. Both phenomena can be traced back to failures in locality properties of boundaryselds { see =-=[44,45]-=- for the case of moduli { so that there exists a direct connection between the brane's intrinsic \fuzziness" and the way it \perceives" its ambient target. Acknowledgements: We would like to thank I. ...

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...〉. 21Since the tachyon profile T(X) is an element of the SU(2) algebra, and |j, m〉 transforms in the (j, m) representation of SU(2) algebra, the non-trivial part of the boundary state becomes simply =-=[18, 20, 21]-=- |B〉 x0 = ∑ j∑ D j m,−m(R)|j, m, m〉〉 , (95) j=0, 1 2 ,··· m=j where D j m,−m(R) is the spin j representation matrix of the rotation R in Jz eigenbasis (see [21] for an explicit form) . To find the bou...

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...g field configuration corresponding to switching on this marginal deformation. In particular, this includes deformations which create a tachyonic lump on a circle of unit radius. As discussed in refs.=-=[23, 24, 15, 16]-=-, if we consider a D-p-brane of bosonic string theory with one of its tangential directions x compactified on 5a circle of radius R, and switch on background tachyon field proportional to cos(x/R), t...