More rings to rule them all: fragmentation, 4<i>D</i>↔ 5<i>D</i>and split-spectral flows

Arsiwalla, Xerxes D.

doi:10.1088/1126-6708/2008/02/066

Cited by 2 publications

(4 citation statements)

References 34 publications

(142 reference statements)

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“…These shifts from the actual brane charges have been shown in [39] to be manifestations of spectral flow when k I = p I . In this way the above relations also serve as a 4D/5D map between the two-center system of a D0-D2-D4 black hole in 4D, placed in the vicinity of a D6-charge; and a black ring in 5D.…”

Section: Jhep09(2009)059mentioning

confidence: 79%

“…Hence we get 5 These are precisely the left-movers of the dual (0, 4) SCFT [25]. 6 The 4D/5D lift for black rings is in fact a special case of spectral flow transformations when the value of k I is set to p I [39].…”

Section: Jhep09(2009)059mentioning

confidence: 95%

“…In section 4 we shall see that this is because of a slight discrepancy that enters the charges defined in [11]. Nevertheless the final 4D and 5D entropies reconcile despite the fact that F br 5 and F br 4 differ due to explicit gauge transformation parameters and also that the observable 5D charges are Page charges whereas the 4D ones are Maxwell [35,39]. This illustrates the point that for a 5D action which includes Chern-Simons terms, there is another way besides a dimensional reduction to 4D; a direct 5D calculation will also give the correct result once the right 5D variables have been implemented into the calculation.…”

Section: Jhep09(2009)059mentioning

confidence: 96%

“…The physical interpretation of spectral flow for black rings has been discussed in [39]. The 4D/5D transformations themselves are in fact a special case of spectral flow transformations.…”

Section: Jhep09(2009)059mentioning

confidence: 99%

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Entropy functions with 5D Chern-Simons terms

Arsiwalla¹

2009

J. High Energy Phys.

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In this article we reconsider Sen's entropy function analysis for 5D supergravity actions containing Chern-Simons terms. The apparent lack of gauge invariance is usually tackled via a 4D reduction. Here we motivate how a systematic 5D procedure also works. In doing so, it becomes important to identify the correct 5D charges. In particular, we perform explicit calculations for the black ring and 5D black hole. In the black ring analysis, we find Chern-Simons induced spectral flow shifts emerging out of Sen's formalism. We find that the entropy function nevertheless remains gauge invariant and the resulting electric charges are identified as Page charges. For the black hole too, 5D gauge invariance is confirmed. Our 5D analysis enables us to fix a mismatch that arose in the electric charges of Goldstein and Jena's 4D-reduced calculation. Finally we provide an interpretation for the e 0 ↔ p 0 exchange in the entropy function as an interpolation between black hole and black ring geometries in Taub-NUT.

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Section: Jhep09(2009)059mentioning

confidence: 79%

Section: Jhep09(2009)059mentioning

confidence: 95%

Section: Jhep09(2009)059mentioning

confidence: 96%

“…The physical interpretation of spectral flow for black rings has been discussed in [39]. The 4D/5D transformations themselves are in fact a special case of spectral flow transformations.…”

Section: Jhep09(2009)059mentioning

confidence: 99%

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Entropy functions with 5D Chern-Simons terms

Arsiwalla¹

2009

J. High Energy Phys.

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On the operator origins of classical and quantum wave functions

Arsiwalla,

Chester,

Kauffman

2023

Quantum Stud.: Math. Found.

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We investigate operator algebraic origins of the classical Koopman–von Neumann wave function $$\psi _{KvN}$$ ψ KvN as well as the quantum-mechanical one $$\psi _{QM}$$ ψ QM . We introduce a formalism of Operator Mechanics (OM) based on a noncommutative Poisson, symplectic, and noncommutative differential structures. OM serves as a pre-quantum algebra from which algebraic structures relevant to real-world classical and quantum mechanics follow. In particular, $$\psi _{KvN}$$ ψ KvN and $$\psi _{QM}$$ ψ QM are both consequences of this pre-quantum formalism. No a priori Hilbert space is needed. OM admits an algebraic notion of operator expectation values without invoking states. A phase space bundle $${{\mathcal {E}}}$$ E follows from this. $$\psi _{KvN}$$ ψ KvN and $$\psi _{QM}$$ ψ QM are shown to be sections in $${{\mathcal {E}}}$$ E . The difference between $$\psi _{KvN}$$ ψ KvN and $$\psi _{QM}$$ ψ QM originates from a quantization map interpreted as “twisting” of sections over $${{\mathcal {E}}}$$ E . We also show that the Schrödinger equation is obtained from the Koopman–von Neumann equation. What this suggests is that neither the Schrödinger equation nor the quantum wave function are fundamental structures. Rather, they both originate from a pre-quantum operator algebra. Finally, we comment on how entanglement between these operators suggests emergence of space; and possible extensions of this formalism to field theories.

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More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

Cited by 2 publications

References 34 publications

Entropy functions with 5D Chern-Simons terms

Entropy functions with 5D Chern-Simons terms

On the operator origins of classical and quantum wave functions

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