Knot invariants and M-theory: Hitchin equations, Chern-Simons actions, and surface operators

Dasgupta, Keshav; Díez, Verónica Errasti; Ramadevi, P.; Tǎtar, Radu

doi:10.1103/physrevd.95.026010

Cited by 6 publications

(188 citation statements)

References 65 publications

(400 reference statements)

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“…Finally, we have also fixed the structures of fermionic corrections and also found couplings to all orders in the world volume of D-brane-Anti-D-brane system. Note that localization method was also used to deal with effective actions [55] and various fermionic interactions in the presence of Anti D3-branes for different fluxes have been discovered as well [56].…”

Section: Resultsmentioning

confidence: 99%

All order α′ corrections to fermionic couplings of D-brane-Anti-D-brane effective actions

Hatefi

2019

J. Cosmol. Astropart. Phys.

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We first point out to all order α ′ corrections to lower order fermionic couplings and their effective actions of type II super string theory. In order to reveal all symmetries of the particular D-brane Anti-D-brane system, and to construct not only all the singularity structures but also all order α ′ corrections of fermionic couplings to tachyons, we employ all the Conformal Field Theory (CFT) methods to a six point function. Basically, we construct all the correlation functions of four spin operators and two world sheet fermion fields. The S-matrix of two fermion fields, two real tachyons in the presence of a closed string Ramond-Ramond (RR) field in type II will be explored. Applying all the symmetries of the amplitude, a proper expansion for D-brane Anti D-brane is also found out.Having carried out all the Effective Field Theory (EFT) techniques, one would discover all order singularity structures of string theory. The entire algebraichave also been derived. Various new string couplings are revealed as well. Eventually, making comparison the S-matrix with all EFT parts, all order α ′ higher derivative corrections to two fermions-two tachyons in the world volume of Dbrane Anti D-brane of type II are discovered accordingly. 1

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Section: Resultsmentioning

confidence: 99%

All order α′ corrections to fermionic couplings of D-brane-Anti-D-brane effective actions

Hatefi

2019

J. Cosmol. Astropart. Phys.

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“…All-order α corrections could grant a firmer quantitative control on vacuum stability in the presence of anti D-branes. This issue which has been thoroughly 18 For a discussion of all-order fermionic couplings for flux backgrounds in the presence of D3-branes, see [65]. 19 For an example where stringy effects in D-brane dynamics play an important role in holography, see [66].…”

Section: Discussionmentioning

confidence: 99%

On all-order higher-point Dp–D̄p̄ effective actions

Antonelli

Basile

Hatefi

2019

J. Cosmol. Astropart. Phys.

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In this paper we derive a class of contributions to all orders in α to the effective action of D-braneanti D-brane systems in Type II String Theory, considering an amplitude involving a closed-string Ramond-Ramond state and four open-string states: two tachyons, a scalar and a gauge boson. This type of amplitude arises in both Type IIA and Type IIB strings, and reveals a number of new effective couplings. Furthermore, we derive a series representation for the result that goes beyond a factorized limit that was recently studied, and which is expected to apply to more general six-point amplitudes of superstrings, including external fermions. * Electronic address: riccardo.antonelli@sns.it † Electronic address: ivano.basile@sns.it ‡ Electronic address: ehsan.hatefi@sns.it 1 For in-depth discussions of open strings, see [1]. 2 For earlier detailed treatments, see [2-4]. 3 Similar corrections can also be found in the case of S-branes [7]. 3 are not present. Perturbative scattering amplitudes involve structures that are largely constrained, which makes it possible to reconstruct them, up to an overall coefficient, via Effective Field Theory (EFT) analyses of poles and symmetries in various channels. On the other hand, ab-initio computations of the corresponding string amplitudes have the virtue of fixing the α expansion, and thus the EFT couplings, to all orders. This procedure has been followed systematically in the literature [33-38], yielding generalizations of the standard Dirac-Born-Infeld (DBI), Myers [39] and Wess-Zumino (WZ) terms 4 [40]. The crucial interplay between D-branes and RR potentials has been thoroughly studied in the literature [42], but theirrole is yet to be fully dissected.The paper is organized as follows. In Section 2 we summarize a number of results that were obtained in earlier works, which provides a starting point for our considerations.Specifically, we discuss all-order α corrections to couplings that originate from amplitudes a single closed-string mode and less than four open-string ones. We focus on RR closed-string states, and thus on couplings related to WZ terms. In Section 3 we present the new result on the five-string scattering amplitude under consideration. From the point of view of the (open) world-sheet CFT, this is akin to a six-point correlator, whose vertex operators are to be integrated accordingly. The result is organized in terms of a class of integrals, whose detailed study is postponed to Section 4. In Section 3.3 we briefly discuss a factorized limit in which the integrals can be evaluated in closed form. In sections 3.4 and 3.5, after a proper discussion of bulk singularities, selection rules [43] and EFT methods, we recover the result from the low-energy perspective. In Section 4 we go beyond the factorized limit of Section 3.3, obtaining an expansion for the integrals, whose leading term reproduces it.While the resulting expansion entails a limit of series with decreasing convergence rate, weshow that the procedure is well-defined. We conclude in Section 5 with a su...

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“…This paper and [13] constitute the first step in the path of computing knot invariants from M-theory, compactified down to four dimensions. We here lay the (fertile) ground for embedding knots in our setting.…”

Section: Introductionmentioning

confidence: 99%

“…We here lay the (fertile) ground for embedding knots in our setting. The simplest knot invariant, the so-called linking number, is computed in [13]. We leave the realization of more challenging invariants to the sequel.…”

Section: Introductionmentioning

confidence: 99%

Knot invariants and M-theory: Proofs and derivations

Díez

2018

Phys. Rev. D

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We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We show that this theory has indeed all required properties to host knots. Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. This is a companion paper to K. Dasgupta, V. Errasti Díez, P. Ramadevi, and R. Tatar, Phys. Rev. D 95, 026010 (2017), covering all but Sec. III C. It presents a detailed mathematical derivation of the main results there, as well as additional material. Among the new insights, those related to supersymmetry and the topological twist are highlighted. This paper offers an alternative, complementary formulation of the contents in the first paper, but is self-contained and can be read independently.

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Knot invariants and M-theory: Hitchin equations, Chern-Simons actions, and surface operators

Cited by 6 publications

References 65 publications

All order α′ corrections to fermionic couplings of D-brane-Anti-D-brane effective actions

All order α′ corrections to fermionic couplings of D-brane-Anti-D-brane effective actions

On all-order higher-point Dp–D̄p̄ effective actions

Knot invariants and M-theory: Proofs and derivations

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