Questions tagged [supergravity]
Supergravity is a classical supersymmetric unification theory that appears in low-energy classical limits of string theory.
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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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CPT Symmetry and the CPT Conjugate in Supersymmetry
Consider a supersymmetric theory in $D=4$ dimensions with $\mathcal{N}$ supercharges, $Q^I_\alpha, \bar{Q}^I_{\dot{\alpha}}.$ When one builds massless particle representations of the SUSY algebra, one ...
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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 ...
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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 ...
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Can this SUSY anomaly disappear in higher dimensions?
I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects.
Explicit breaking of supersymmetry ...
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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 ...
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References about supersymmetry in $d=3$
Most references on supersymmetry and superspace focus on $d=4$. Can someone suggest references about superspace in $d=3$? Given the new importance of superconformal field theories in $d=3$, I want to ...
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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$$ ...
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Dimensional reduction of supermultiplets
Consider the (10d) IIA supergravity multiplet: (in terms of $SO(8)$ representations) a graviton $\boldsymbol{44}$, a 1-form $\boldsymbol{8}_V$, a 2-form $\boldsymbol{28}$, a 3-form $\boldsymbol{56}_V$,...
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What is the problem with classical fermionic field?
Consider classical fermionic field. We have it's action, equations of motion and so we can get it's solutions, right?
For example, we can consider gravitational solutions with fermions (in particular, ...
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Supergravity in our universe of accelerated expansion
In "On supergravity theories, after ~40 years" (Jean-Pierre Derendinger) presented on DISCRETE 2014" it is said (p.16) that a positive cosmological constant is not compatible with ...
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Kaluza-Klein reducing the Chern-Simons term in 11D supergravity
In 11D supergravity we have the Chern-Simons term of the 3-form field $C$
\begin{equation}
\int C \land d C \land d C
\end{equation}
I want to consider this on a spacetime $\mathbb{R}^{1,6}\times S$ ...
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Charge conjugation of symplectic Majorana spinors in 4+1 dimensions
In the book "Supergravity" written by Freedman & van Proeyen, a symplectic Majorana spinor is defined in eq. (3.86)
$$ \chi^i = \varepsilon^{ij} (\chi^j)^C, \tag{3.86}$$
where the upper ...
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Is the 11th dimension in M-theory a line or a circle?
I'm familiarizing myself with $M$-theory and I think I get the big picture now, but I've read different accounts on this. According to some expositions by people that I think know what they are ...
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Is the black brane picture valid only at small string coupling?
As far as I am aware there are two pictures of branes:
for $g_SN\gg1$: branes as solitonic solutions to the field equations of supergravity (i.e. black branes)
for $g_SN\ll1$: branes as fundamental ...
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How to Wick rotate differential forms?
The bosonic sector of the Cremmer-Julia-Sherk (CJS) 11D supergravity action is
$$ eR-\frac12 F\wedge *F-\frac16 A\wedge F\wedge F,$$
where $F=dA$ is a 4-form field strength.
How would one perform a ...
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MAGOO 2-Point Correlation function derivation
I am studying the famous MAGOO review and I am trying to understand section 3.3 where we calculate the correlation functions from the AdS side. In subsection 3.3.1 the authors go through the 2-point ...
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Anti-de Sitter superalgebra from preserved symmetry
Following Freedman & Van Proeyen's "Supergravity", the $\mathcal{N}=1,\, D=4$ AdS supergravity action is
$$ \dfrac{1}{2\kappa^2}\int d^4x \; e \left[R(\omega) - \bar{\psi}_\mu \gamma^{\...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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:
$$ H^2 = \frac{8\pi}{3m_{pl}^2} \rho + \...
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Deriving an action from a metric
I try to find out how in this paper
https://arxiv.org/abs/hep-ph/9905221
the authors derived an effective action from the metric.
The paper I study is related to string theory and modified gravity ...
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Symplectic Majorana spinors in 5D
According to the book "Supergravity" written by Freedman & van Proeyen in 5D for the existence of Majorana spinors it is necessary to introduce so called sympletic ones which requires
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Can I just add a cosmological constant to an on-shell supergravity action?
Suppose one has some supergravity Lagrangian $\mathcal{L}_\text{sugra}$ in flat (Minkowski) space. Moreover, assume that this Lagrangian is on-shell, in the sense that the auxiliary fields have been ...
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Supergravity 3-form $C$ fields from 2d string worldsheets
In supergravity, there are 3-form fields known as C fields.
However, according to string theory, the fundamental degrees of freedoms are from string worldsheets (so at most they are fundamentally 2d).
...
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Modification of Riemann tensor by twisting the spin connection
Suppose one has a funfbein $e^a_{\mu}$ with associated spin connection $\omega^\mu_{\,ab}$. Writing this in terms of differential forms,
$$e_a:=e_a^{\mu}\mathrm{d}x^{\mu},\ \ \ \omega_{ab}:=\omega^\...
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Is Supergravity just Super String Theory without open strings?
I'm trying to understand the elements of the AdS-CFT correspondence. The definition I have in mind is a correspondence between:
(A) a Super String Theory of $D_p$-branes and closed strings in a $10$d ...
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What is a protected states in Supersymmetry, Superstring theory context
I know that they are the states that have protected scaling dimension when couplings are changed. But there are some states that are protected only in free orbifold theory, this is something I don't ...
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What is "string universality"?
I encountered the notion of "string universality" in the TASI lectures on Supergravity (April 2011). What does this actually mean? Does it mean that every consistent (in particular ...
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Is there a Lagrangian for Super-Gravity?
Einsteins field equations can be derived from the Einstein-Hilbert action which only involves the scalar curvature $R$ of the spacetime manifold. This is simply
$$S = \int_M R.$$
The volume form or ...
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Which non-homogeneous scalar manifolds are possible in supergravity?
The scalar fields in various supergravity theories are restricted (by supersymmetry) to span the target (scalar) manifolds of a certain class (e.g. Hodge-Kahler, quaternion-Kahler etc.), depending on ...
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Gauging $R$-Symmetry
I know that if one gauges the supersymmetry group, you get supergravity. You can then further gauge the $R$-symmetry and these are the so-called gauged supergravities. But I don't think I've seen ...
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Precise zero energy bound for supersymmetry
Usually we can shift the energy $E$ by any amount $\delta$ to redefine the lowest energy as
$$
E + \delta.
$$
However, in supersymmetry, there is a precise $E=0$ must be true, so that the supercharge $...
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STU supergravity
Tghere are a lot of different papers about STU supergravity, for example see this.
As I understand, STU supergravity is N = 2 supergravity coupled
to three vector multiplets.
Could someone explain, ...
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Dimensional reduction with supermanifolds and gravity
When having compact dimensions (I guess it is not true with supermanifolds), the gravitacional constant gets diluted in extra dimensional space:
$$G_N(4d)=G_N(Dd)/V(X)$$
However, I presume that the ...
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Why is 11 Dimensional SUGRA not a consistent quantum theory?
I am studying the $S$ duality between 11D supergravity and type IIA superstring theory from Adel Bilal’s paper. The author says:
Of course, eleven dimensional supergravity is not expected to yield a ...
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Kaluza-Klein supermultiplet of 11D supergravity
I am studying Adel Belali's review paper "M(atrix) theory: a pedagogical introduction" for my undergraduate thesis. In the third lecture, part one, we dimensionally reduce 11D supergravity ...
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