Romans Massive QP Manifolds
Abstract
:1. Introduction
2. QP Manifolds for IIA Branes
2.1. D2 ( Algebroid)
- 1
- For , the identities arising from correspond precisely to Bianchi identities and field equations for the fluxes of massive type IIA with the conventions of [6].
- 2
- The field can naturally be viewed as a gauge connection for a gauge transformation generated by rescalings , . For these transformations to still satisfy (3) then we also need to shift . Putting this into (5), we see that this has the effect of transforming . The constraint (11) then just says that this is a flat connection. Flat connections on gauge bundles are always gauge trivial. That is, we can always pick a gauge where globally. Hence, this is classically equivalent to the massive IIA Bianchi identities.
2.2. D4 ( Algebroid)
- 1
- Setting , we recover the Bianchi identities for massive IIA supergravity.
- 2
- is a flat connection coming from the same rescaling gauge symmetry. The charges of all the fluxes under this are different, however, to the D2 algebroid.
2.3. NS5 ( Algebroid)
- 1
- Setting , we recover the Bianchi identities for massless IIA supergravity. This is always possible as is a flat connection.
- 2
- Note that, unlike the D2 and D4 branes, we do not have the Romans mass appearing here. Viewing the Romans mass as the flux of the D8 brane, we note that the NS5 brane only couples to the D8 brane via a D6 brane [17]. Our construction here, however, does not include any D6 branes since we have no flux. We therefore, do not expect that the QP manifold for NS5 branes would allow for massive deformations and this is indeed what we find.
3. IIA/M-Theory Duality
3.1. M5 to NS5
3.2. M2 to D2
4. Applications
4.1. AKSZ Models
4.1.1. D2 Brane
4.1.2. NS5 Brane
4.2. The (Topologically Massive) D2 Brane Phase Space
5. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
1 | A supermanifold with an extra -grading on its structure sheaf, so all functions f have a well-defined degree ; for us, and equal the Grassmann parity, and this grading is equivalent to the existence of a degree-counting vector field (“Euler”), which we employ later. |
2 | The anchor map is intrinsic to the definition of these higher algebroids; see, e.g., [1]. |
3 | A priori, one could have terms such as and . However, we will assume that is invertible, which is equivalent to saying that the anchor map associated to the algebroid is surjective. Hence, one can always perform a canonical transformation to set and . |
4 | The necessity of performing asymplectomorphism before the symplectic reduction was also observed in [18]. |
5 | In double field theory, Romans IIA theory arises by giving the Ramond–Ramond fields a linear dependence on the dual coordinates [22]. |
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Arvanitakis, A.S.; Malek, E.; Tennyson, D. Romans Massive QP Manifolds. Universe 2022, 8, 147. https://doi.org/10.3390/universe8030147
Arvanitakis AS, Malek E, Tennyson D. Romans Massive QP Manifolds. Universe. 2022; 8(3):147. https://doi.org/10.3390/universe8030147
Chicago/Turabian StyleArvanitakis, Alex S., Emanuel Malek, and David Tennyson. 2022. "Romans Massive QP Manifolds" Universe 8, no. 3: 147. https://doi.org/10.3390/universe8030147
APA StyleArvanitakis, A. S., Malek, E., & Tennyson, D. (2022). Romans Massive QP Manifolds. Universe, 8(3), 147. https://doi.org/10.3390/universe8030147