On functions of bounded n-th variation

Mukhopadhyay, Sourangshu; Sain, Debmalya

doi:10.4064/fm-131-3-191-208

Cited by 7 publications

(24 citation statements)

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“…( 2.2) This result poses a puzzle as defining the EM tensor according to PNO would imply that the theory does not have a smooth flat-space limit. This, as we will explain below, is contradictory with the universality property discussed in [16,17]. Let us consider an on-shell pp-wave background with flat transverse space in string theory.…”

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confidence: 85%

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String worldsheet theory in hamiltonian framework and background independence

Mukhopadhyay

2013

J. Phys.: Conf. Ser.

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Abstract. We analyze exact conformal invariance of string worldsheet theory in non-trivial backgrounds using hamiltonian framework. In the first part of this talk we consider the example of type IIB superstrings in Ramond-Ramond pp-wave background. In particular, we discuss the quantum definition of energy-momentum (EM) tensor and two methods of computing Virasoro algebra. One of the methods uses dynamical supersymmetries and indirectly establishes (partially) conformal invariance when the background is on-shell. We discuss the problem of operator ordering involved in the other method which attempts to compute the algebra directly. This method is supposed to work for off-shell backgrounds and therefore is more useful. In order to understand this method better we attempt a background independent formulation of the problem which is discussed in the second half of the talk. For a bosonic string moving in an arbitrary metric-background such a framework is obtained by following DeWitt's work (Phys. Rev.85:653-661,1952) in the context of particle quantum mechanics. In particular, we construct certain background independent analogue of quantum Virasoro generators and show that in spin-zero representation they satisfy the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. We also report on a new result which states that the same algebra holds true in arbitrary tensor representations as well. Introduction and summaryThis talk will be based on the papers [1, 2, 3, 4] and certain new results in [5]. In [1, 2, 3] we try to understand exact conformal invariance of string worldsheet theory in certain ppwave backgrounds using hamiltonian framework 1 . Usually backgrounds that are nearly flat are considered for such analysis. The reason is that for flat background the theory is exactly solvable and the relevant vacuum is known. One can then define the quantum EM tensor in the weak background field approximation by normal ordering the interaction terms with respect to the flat-space-vacuum. The pp-wave background on the other hand is not close to flat and therefore the corresponding worldsheet theory is strongly interacting. We will discuss this problem in section 2.The end result of the analysis in section 2 will show that there exists an operator ordering ambiguity in the computation of the Virasoro anomaly if one tries to calculate them directly using the quantum EM tensor. In order to have a better understanding of the situation we seek a framework where the computations can be done in a background independent way. Such a framework was developed by DeWitt in [10] for particle quantum mechanics. As will be

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confidence: 85%

“…This is done by suitably generalizing DeWitt's argument in [10]. The result is given by, 15) where 16) δ(x −x) being the Dirac delta function, g = |detg ij |, 3.17) where ∇ k is the covariant derivative with respect to x k and…”

Section: Higher Rank Tensor Generalizationmentioning

confidence: 99%

String worldsheet theory in hamiltonian framework and background independence

Mukhopadhyay

2013

J. Phys.: Conf. Ser.

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“…The calculation of their normalization constant was given in [20]. Subsequently, the general properties of the type IIB boundary states were analysed in [14,15,20,21,22,23,24] and that of the type IIA boundary states were studied in [25,26,27,28,29,30,31,32,33,34,35] . Thus, the existence of the thermal string, on one hand, and of the coherent state representation of D-branes, on the other hand, suggests the existence of a relationship between the thermalized string states and the thermalized D-brane boundary states in the pp-wave background analogous to the one in the flat spacetime [36].…”

Section: Introductionmentioning

confidence: 99%

THERMAL D-BRANE BOUNDARY STATES FROM TYPE IIB GREEN–SCHWARZ SUPERSTRING IN pp-WAVE BACKGROUND

Vancea

2008

Int. J. Mod. Phys. A

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We construct the thermal boundary states from the type IIB Green-Schwarz superstring in pp-wave background in the light-cone gauge. The superstring is treated in the canonical ensemble and in the TFD formalism which is appropriate to discuss canonically quantized systems. The thermal boundary states are obtained by thermalizing the total boundary states which are the boundary states of the total system that is composed by the superstring modes and the corresponding thermal reservoir modes. That analysis is similar to the one in the flat spacetime case [67]. However, there are some subtleties concerning the construction of the total string which are discussed. Next, we compute the entropy of thermal boundary state which is defined as the expectation value of the superstring entropy operator in the thermal boundary state. * ionvancea@ufrrj.br

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“…We may further suppose that each element of E is less than every element of F. Let {(c w , <£")} be any sequence of non-overlapping intervals with end points on EUF. The only case that needs to be considered is c v £ E, d v £ F for some v, since in all other cases and hence •, d p )\ [6] where ai, f3i are positive numbers such that Hence (dp-c p )\Qk{f;c p , i u ..., ^f c _i,(fp)| …”

Section: (E)mentioning

confidence: 99%

“…(For a different approach we refer to [6]). The concept of a generalised Lipschitz condition of order fc is also introduced.…”

Section: Introductionmentioning

confidence: 99%