Download PDF by Vincent Rivasseau (Chief Editor): Annales Henri Poincaré - Volume 4 - Supplements
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Additional info for Annales Henri Poincaré - Volume 4 - Supplements
Nevertheless defects in the ﬁeld can survive and describe non-trivial objects in the (9+1)-dimensional space-time in which full string theory lives. There are also other more complicated examples of ‘tachyonic defects’. For ¯ pair describes a BPS D-(p − 2)-brane example, a vortex solution on a Dp-Dp . On the other hand, a ’t Hooft Polyakov monopole on a pair of coincident non-BPS Dp-branes describes a non-BPS D-(p − 3)-brane . In this way all D-branes can be regarded as defects in the tachyon ﬁeld living on D-branes of maximal dimension.
18) 0 x 1 This matrix has the property that for a generic Majorana matrix M one ﬁnds: 0 0 0 . (19) mν = mTD M −1 mD ∝ 0 x2 x 0 x 1 The only condition on M −1 is that the 33 entry is non zero. But when the approximately vanishing matrix elements are replaced by small terms, one must also assume that no new o(1) terms are generated in mν by a compensation between small terms in mD and large terms in M . It is important for the following discussion to observe that mD given by eq. (15) under a change of basis transforms as mD − > V † mD U where V and U rotate the right and left ﬁelds respectively.
In the case of a conventional scalar ﬁeld, if we displace the ﬁeld from its maximum and let it roll down the potential, the scalar ﬁeld will oscillate about its minimum. Energy-momentum tensor Tµν for this solution will have the form: T00 = E, Tij = −p(x0 )δij , Ti0 = 0 . (6) S38 Ashoke Sen Ann. Henri Poincar´e Here E denotes the energy density, and remains constant due to energy conservation. p denotes the pressure, and will typically oscillate about an averge value (0 for a conventional scalar ﬁeld) as the scalar ﬁeld oscillates about its minimum.
Annales Henri Poincaré - Volume 4 - Supplements by Vincent Rivasseau (Chief Editor)