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...hat only the transverse traceless part of the determinant is considered, and the index (s) refers to the spin. (As before, ℓ is the AdS radius.) Determinants of this form were explicitly evaluated in =-=[44]-=- using group theoretic techniques; applying these results to the present context one finds that the 1- loop answer factorises nicely into left and right moving pieces Z1−loop(s) = ∞∏ n=s 1 |1− qn|2 , ...

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...but does not confirm the identity of partition functions. 2. The gravity partition function Let us begin by calculating the 1-loop contribution of the bulk degrees of freedom. Using the techniques of =-=[24]-=- the contribution of a massless spin s field to the 1-loop partition function on thermal AdS3 was found to be [23] Zspin s = ∞∏ n=s 1 |1− qn|2 . (2.1) Combining the contributions from the fields of ev...

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...er of generators at each spin becomes roughly doubled. 5 which follows from the spectrum mentioned above. For a complex scalar with dual conformal dimension (h, h), the one-loop partition function is =-=[42, 43]-=- Zhscalar(q) = ∞∏ m,n=0 1 (1− qh+mq̄h+n)2 , (2.4) and for a Dirac fermion with dual conformal dimension (h, h− 1/2), (h− 1/2, h) it is [41] Zhspinor(q) = ∞∏ n,m=0 ( 1 + qh+mq̄h+n−1/2 ) ( 1 + qh+m−1/2q...

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... route packets among different devices. Transport protocol(s)sRouting protocolssAP1sMACsWireless InterfacesAP2 …sFigure 6.1: System components of an ad hoc testbed In the current Linux implementation =-=[92]-=-, socket layer interface implemented in the kernel provides a standard API which allows user space programs to open a communication endpoint to a remote device. The implementations of transport layer ...

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... route packets among different devices. AP1 AP2 … Transport protocol(s) Routing protocols MAC Wireless Interface Figure 6.1: System components of an ad hoc testbed In the current Linux implementation =-=[92]-=-, socket layer interface implemented in the kernel provides a standard API which allows user space programs to open a communication endpoint to a remote device. The implementations of transport layer ...

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... Communication in Linux If one process exchanges data with another process, it is called interprocess communication (IPC). Linux oers a variety of mechanisms for IPC. These are the following listed: =-=[23]-=- Signals Oldest IPC method. A process can send signals to processes with the same uid and gid or in the same process group. Pipes Pipes are unidirectional bytestreams that connect the standard output ...

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... s field these involve Laplacians for transverse traceless modes of helicity ±s as well as – 2 – ±(s− 1) Z(s) = [ det ( −∆+ s(s− 3) ℓ2 )TT (s) ]− 1 2 [ det ( −∆+ s(s− 1) ℓ2 )TT (s−1) ] 1 2 . (1.2) In =-=[12]-=- such determinants were explicitly evaluated, in a thermal background, for arbitrary spin s, using the group theoretic techniques of [13, 14]. By applying the results of [12] we find that the one loop...