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Questions tagged [supergravity]

Supergravity is a classical supersymmetric unification theory that appears in low-energy classical limits of string theory.

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How do I obtain the low energy supergravity actions from the 5 superstring theories?

In Domain-Walls and Gauged Supergravities by T.C. de Witt, there is a small table giving the 5 string theories and each of their effective sugras. I am looking for detailed reviews of how these sugras ...
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Can Black Holes with electroweak or strong interactions exists in General Relativity or in Supergravity?

During my Master's degree, we studied Black Holes as solutions of Einstein-Maxwell equations, and I was wondering if it would be possible to also add strong or electroweak forces in the classic non-...
Aleph12345's user avatar
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Graded cyclic properties in tensor calculus formalism of supergravity

I am trying to understand the chapter 4 of https://arxiv.org/abs/hep-th/0204035. I want to obtain equation 4.19 in this article. First let me summarized some equations we need Denoting the gauge ...
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Prepotential in 5d $\mathcal{N}=1$ with higher-derivative correction

The (bosonic part of the) action of five-dimensional $\mathcal{N}=1$ supergravity coupled to a number of vector multiplets reads $$S=\frac{1}{2\kappa_5^2}\int\star(R-\frac{1}{2}h_{ij}(\phi)\partial-\...
TwoStones's user avatar
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How to decompse kinetic term operator in string compactification

In general textbook, when we want to calculate the dimension of moduli space of string compactification, i.e. calculate the number of massless modes after dimension reduction, we use the following ...
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Introductory Reference for Supergravity

I have finished quantum field theory and general relativity and want to read about supergravity. I have read about supersymmetry from the demystify series and the supersymmetry part of Wess and Bagger'...
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The Role of the Kaehler Manifold in Supergravity

Actually, I already asked a similar question Coupling of supergravity to matter which has remained unanswered. So this time I will be less general. In the very interesting paper arXiv:2212.10044 [...
Frederic Thomas's user avatar
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Why do spherical M2 branes have no net charge?

In the paper Invasion of the Giant Gravitons from Anti de Sitter Space, the authors claim that We are interested in the dynamics of a relativistic spherical membrane moving in $S^4$. The membrane has ...
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Computing equations of motion for type IIB supergravity

I'm doing some introductory calculations on the D3-brane solution of type IIB supergravity. I'm considering the theory with action $$S_{\text{IIB}} = \frac{1}{8\pi G_{10}}\int d^{10}z\sqrt{g_{10}}\...
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Unitarity in the 't Hooft limit

Consider a quantum gauge theory with a holographic dual at infinite $N$ and 't Hooft coupling, in which the gauge theory is described by classical (super)gravity. If I initialize the system in a pure ...
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Why are $E_{d(d)}$ representations labelled by integers?

Reducing 11d supergravity on a torus $T^d$ or, equivalently, IIB supergravity on $T^{d-1}$, one gets an exceptional $E_{d(d)}$ hidden symmetry, which is, in particular, the non-compact split real form ...
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Why do the scalars always occupy the coset they do?

If I reduce a $D$-dimensional theory on a $d$-dimensional manifold $M_d$, then I will be left with some reduced, effectively $(D-d)$-dimensional theory with some global symmetry group $G$. In general, ...
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Local Supersymmetry and Space-time Metric

So following from Simple Supergravity (arxiv:2212.10044), on page 5, it's written that Only the spacetime metric can couple to the energy-momentum tensor... Can anyone explain why it must be the ...
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What are Bubbling Geometries?

I know that Wilson loops in certain higher rank representations are dual to Bubbling Geometries. Also, certain local operators are dual to this kind of solutions. But (independently from holography), ...
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Ground state vertex operator in superstring theory

In Tongs' "String Theory" lectures chapters 5.4.1-5.4.2 Tong referred to alternative way to find the mass of the different string states using suitable operators, and then integrating the ...
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Spin 3/2 field in higher dimensions

The Lagrangian and equation of spin 3/2 field in a general dimension D is given on page 96 of Supergravity ( textbook by Freedman and Proeyen, 2012 ). The action is : $$ S = - \int d^Dx \bar{\psi}_{\...
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Coupling spin 3/2 fields with electromagnetism (causally)

I am trying to read literature regarding the coupling of massive spin-$\frac{3}{2}$ fields with electromagnetism. Apparently, an elementary (i.e. not composite) massive spin-$\frac{3}{2}$ field can't ...
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Variation of Torsion-Free Spin Connection

In the book 'Supergravity' by Freedman and van Proeyen, in exercise (7.27) it is written To calculate [the variation $\delta\omega_{\mu ab}$ of the torsion-free spin connection], consider the ...
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How to construct the final action for a supergravity theory $N = 1$ in 4D?

I am trying to understand the basics of supergravity theory $N = 1$ in 4D, which combines supersymmetry and general relativity. I know that the theory involves a spin 2 field whose quantum is the ...
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Predicted Mass of Hypothetical Graviphoton

In (some) supersymmetry theories, a spin-1 gravivector or graviphoton is predicted (but has not yet been observed) to exist. My question: is there a consensus among theorists as to the mass (if any) ...
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Derivation of torsion in supergravity

I am trying to derive the expression for torsion, equation (9.18), in the textbook Supergravity ( by Freedman and Proeyen, 2012 ). The strategy is to vary the Einstein-Hilbert action ( $S_2$ ) and the ...
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Counting number of equations for Rarita-Schwinger field (in Supergravity textbook)

I am reading the book "Supergravity" by Freedman and van Proeyen (2012). On page 96, they are talking about the equation of motion of massless vector-spinor field (the spinor index is ...
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Coupling of supergravity to matter

Whereas the "derivation" of the pure supergravity Lagrangian seems to be rather straightforward, once it comes to combine supergravity with matter, i.e. for instance with an ungauged chiral ...
Frederic Thomas's user avatar
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Gravitino's and vielbein's gauge transformation in Freedman's Supergravity

I'm facing a problem with Ex. 11.7 of Freedman's "Supergravity", specifically about gauge fields and their transformations. At page 218 the authors present a useful list of all structure ...
Fredrigo6's user avatar
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Differences between Einstein Gravity and classical Supergravity?

Given that the main difference of super-spacetime and spacetime is in the Grassmann dimensions, I want to know about the main differences in terms of results and features or modifications, between ...
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Derivatives as "dynamical variables of the theory"?

This question will probably sounds very broad. So, I work with classical general relativity, a bit of field theory and semiclassical gravity. I have a friend, though, that works with things like ...
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Holomorphic sections that lead to the original parameterization of the gauged STU model

The original action, given in 9903214, comes from the $\mathcal{N} = 2$ abelian truncation of the maximal $\mathcal{N} = 8$, $SO(8)$ gauged supergravity that can be obtained from $S^ 7$ reduction of ...
4 votes
1 answer
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Field equations of 11d supergravity in geometrical notation

In 1112.4967, it is stated that the field equations of 11d supergravity are (eq. 24 there) $$\operatorname{Ric}(X,Y)=\frac{1}{2}\langle\imath_XF,\imath_YF\rangle-\frac {1}{6}g(X,Y)\langle F,F\rangle$$ ...
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Dimensional reduction of supermultiplets

Consider the (10d) IIA supergravity multiplet: (in terms of $SO(8)$ representations) a graviton $\boldsymbol{44}$, a 1-form $\boldsymbol{8}_V$, a 2-form $\boldsymbol{28}$, a 3-form $\boldsymbol{56}_V$,...
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What is the problem with classical fermionic field?

Consider classical fermionic field. We have it's action, equations of motion and so we can get it's solutions, right? For example, we can consider gravitational solutions with fermions (in particular, ...
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Supergravity in our universe of accelerated expansion

In "On supergravity theories, after ~40 years" (Jean-Pierre Derendinger) presented on DISCRETE 2014" it is said (p.16) that a positive cosmological constant is not compatible with ...
Frederic Thomas's user avatar
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Kaluza-Klein reducing the Chern-Simons term in 11D supergravity

In 11D supergravity we have the Chern-Simons term of the 3-form field $C$ \begin{equation} \int C \land d C \land d C \end{equation} I want to consider this on a spacetime $\mathbb{R}^{1,6}\times S$ ...
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Charge conjugation of symplectic Majorana spinors in 4+1 dimensions

In the book "Supergravity" written by Freedman & van Proeyen, a symplectic Majorana spinor is defined in eq. (3.86) $$ \chi^i = \varepsilon^{ij} (\chi^j)^C, \tag{3.86}$$ where the upper ...
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Is the 11th dimension in M-theory a line or a circle?

I'm familiarizing myself with $M$-theory and I think I get the big picture now, but I've read different accounts on this. According to some expositions by people that I think know what they are ...
Alexander Praehauser's user avatar
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Is the black brane picture valid only at small string coupling?

As far as I am aware there are two pictures of branes: for $g_SN\gg1$: branes as solitonic solutions to the field equations of supergravity (i.e. black branes) for $g_SN\ll1$: branes as fundamental ...
user56517852's user avatar
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1 answer
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How to Wick rotate differential forms?

The bosonic sector of the Cremmer-Julia-Sherk (CJS) 11D supergravity action is $$ eR-\frac12 F\wedge *F-\frac16 A\wedge F\wedge F,$$ where $F=dA$ is a 4-form field strength. How would one perform a ...
Alex Coglin's user avatar
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MAGOO 2-Point Correlation function derivation

I am studying the famous MAGOO review and I am trying to understand section 3.3 where we calculate the correlation functions from the AdS side. In subsection 3.3.1 the authors go through the 2-point ...
twisted manifold's user avatar
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Anti-de Sitter superalgebra from preserved symmetry

Following Freedman & Van Proeyen's "Supergravity", the $\mathcal{N}=1,\, D=4$ AdS supergravity action is $$ \dfrac{1}{2\kappa^2}\int d^4x \; e \left[R(\omega) - \bar{\psi}_\mu \gamma^{\...
phenolphthalein's user avatar
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Spin-2 operators from metric fluctuations in the AdS/CFT

This is a computational question. I am pretty sure that there is a simple explanation, and something obvious that I am missing but I cannot figure it out. I want to add that this is not meant to be a &...
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Can local supersymmetry be characterized entirely in terms of observables?

Global symmetries can be defined through their effect on observables. In contrast, quantum theories are often constructed with the help of symmetries that leave observables invariant, like the ...
Chiral Anomaly's user avatar
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Confusion about Generating Functionals in AdS/CFT

I have a question regarding an equation in the book "Gauge/Gravity Duality" by Martin Ammon and Johanna Erdmenger which however can also be found in other AdS/CFT books or lecture notes. The ...
olse barn's user avatar
2 votes
1 answer
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Dimensional Reduction and Supersymmetry

I am working my way through "Basic Concepts of String Theory", by Blumenhagen, Lüst and Theisen. Currently I am working on the compactifications of string theories on Calabi-Yau manifolds. ...
maarten442's user avatar
1 vote
1 answer
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The volume of infinitly large extra dimension

What I understand is that, according to the string theory our universe is a membrane parallel to several other membranes or (universes). These parallel universes are separated by the bulk or extra ...
Dr. phy's user avatar
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Constraints on non-compactified extra dimensions

I'm reading this paper An introduction to extra dimensions and string phenomenology Which according to it, in string theory the 4-dimensional Plank scale is related to the Planck scale of ...
Dr. phy's user avatar
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The Hubble parameter of Randall-Sundrum model

It’s mentioned in this paper On the cosmological constant problem and brane-world geometry that the Hubble parameter of the Randall-Sundram model is given by: $$ H^2 = \frac{8\pi}{3m_{pl}^2} \rho + \...
Dr. phy's user avatar
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1 answer
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Deriving an action from a metric

I try to find out how in this paper https://arxiv.org/abs/hep-ph/9905221 the authors derived an effective action from the metric. The paper I study is related to string theory and modified gravity ...
Dr. phy's user avatar
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Symplectic Majorana spinors in 5D

According to the book "Supergravity" written by Freedman & van Proeyen in 5D for the existence of Majorana spinors it is necessary to introduce so called sympletic ones which requires ...
Frederic Thomas's user avatar
1 vote
1 answer
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Can I just add a cosmological constant to an on-shell supergravity action?

Suppose one has some supergravity Lagrangian $\mathcal{L}_\text{sugra}$ in flat (Minkowski) space. Moreover, assume that this Lagrangian is on-shell, in the sense that the auxiliary fields have been ...
arow257's user avatar
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2 votes
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Supergravity 3-form $C$ fields from 2d string worldsheets

In supergravity, there are 3-form fields known as C fields. However, according to string theory, the fundamental degrees of freedoms are from string worldsheets (so at most they are fundamentally 2d). ...
ann marie cœur's user avatar
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Modification of Riemann tensor by twisting the spin connection

Suppose one has a funfbein $e^a_{\mu}$ with associated spin connection $\omega^\mu_{\,ab}$. Writing this in terms of differential forms, $$e_a:=e_a^{\mu}\mathrm{d}x^{\mu},\ \ \ \omega_{ab}:=\omega^\...
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