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

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Symbolic algebra to obtain equations of motion from supergravity actions [duplicate]

While trying to study the classical supergravity solutions, I realized that there's a considerable amount of intermediate tensor algebra involved, and while it is imperative that I work out all the ...
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Why is the torus important for compactification in string theory? (aka much ado about the torus)

Why is the torus important in string theory and supergravity? To be specific, why does one care about something like compactification of Type IIB or IIA supergravity on a torus $T^5$, as opposed to ...
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Basic question about curved and flat indices, and the Dirac matrices on $S^5$

In discussing the Kaluza-Klein formalism for Type IIB Supergravity on $S^5$, or the AdS5xS5 compactification, one requires Killing spinors on $S^5$. I read that the Dirac matrices on $S^5$ satisfy ...
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What does it mean to “uplift” a supergravity solution to higher dimensions?

What does it mean to "uplift" a supergravity solution to higher dimensions? This is a common term used in the literature but I cannot understand it. A very common example is "uplifting d-dimensional ...
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supersymmetry in 7, 8, 9 dimension

Why above dimension (7,8,9) the number of supercharge per supersymmetry is equal? $i.e$ For 32 supercharges, supersymmetry in 7,8,9 dimension is describe by $N=2$. And for 16 supercharges, ...
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supersymmetry in 2,6,10 dimension

Why the susy has chirality in above (2,6,10) dimension? What i am saying is that for $2, 6, 10$ dimension we can write as follows For 2d : $N=(16,16), \cdots N=(2,2), N=(2,0), N=(1,1), N=(1,0)$ are ...
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Type IIB string theory is chiral. Do there exist non-chiral II SUGRA theories?

Type IIB string theory is chiral. Do there exist non-chiral $\mathcal{N}=2$ II SUGRA theories? The answer is apparently yes. Additionally how do we understand the fact that Type IIB SUGRA is chiral ...
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What is the significance of self-duality and anti self-duality in supergravity?

So I see the terms "self-dual" and "anti self-dual" appear routinely in supergravity/string thery, e.g. the fact that Type IIB supergravity contains a real self-dual rank-5 antisymmetric tensor ...
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Is the $\alpha'$ expansion in string theory an asymptotic expansion?

The low-energy bosonic effective actions of string theory lead to Einstein-Hilbert gravity, along with scalars and $p$-form Maxwell fields. For example, the action for type IIA string theory is $S = ...
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Maximal gauged Supegravity [closed]

In a maximal gauged supergravity in five dimension, there is a maximal supersymmetry with local supersymmetry and as R-Symmetry there is a USp(8) group. The condition that supersymmetry is verified ...
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Supergravity prerequisites for branes in string theory [duplicate]

I have a one-semester background in string theory (bosonic string theory, the NSR string, conformal field theory), but I have not taken any full length courses on supersymmetry and supergravity. I'm ...
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What does “local composite symmetry” mean in ${\cal N}=8$ $d=5$ supergravity?

What does it mean "local composite symmetry" in supergravity? Specifically, I don't understand very well the local composite symmetry ${\rm USp}(8)$ in ${\cal N}=8$ $d=5$ supergravity.
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Can a metric in General Relativity, Supergravity, String Theory, etc., be asymmetric?

Why is it that all problems I encountered until now have metrics that when represented in a matrix form turn out to be symmetric? Aren't there asymmetric matrices representing some metrics?
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Super weyl transformation of superfiled R [closed]

Can anyone guide me how to find super weyl transformation of R (main superfield of SUGRA)? I think that I need super weyl transformation of super vielbein and super connection and using the ...
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Supersymmetry transformations as coordinate transformations

Usually, a supersymmetry transformation is carried out on bosonic and fermionic fields which are functions of the coordinates (or on a superfield which is a function of real and fermionic ...
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Why do we need frame-fields to describe fermions in SUGRA?

I'm learning about the frame formalism and read that to couple fermions to gravity you need to go to the frame-formalism. As a motivation to learn more about frame-fields would someone sketch me why ...
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Killing spinor equation [closed]

The Supersymmetry transformation is: $$\delta \psi_\mu^i=(\partial_\mu +1/4 \gamma^{ab}\omega_{\mu ab})\epsilon^i -1/8\sqrt{2}\kappa \gamma^{ab}F_{ab}\epsilon^{ij} \gamma_\mu \epsilon_j$$ For the ...
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breitenlohner freedman stability condition

I am looking for a simple way to derive the breitenlohner-freedman bound. Actually I can't understand why we have stability above the BF bound and instability below the BF bound,while both have ...
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how to specify eigenfunctions(eigentensors) of Lichnerowicz operator?

Lichnerowicz operator is an operator which acts on transverse trace-free symmetric tensors. If this statement is correct, my question is that any transverse trace-free symmetric tensor is an ...
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Supergravity solution, metric for the total space, and connection

In supergravity solutions, one sometimes encounters the case where the manifold may be a bundle over some base space, and one has to write down the explicit metric regarding such bundle. I would like ...
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53 views

why is it important to find stability of supergravity solutions? [closed]

I want to know about the importance of the stability, generally,why is stability important in super-gravity? and why do we like these solutions?
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Calabi-Yau condition, moduli and Lichnerowicz equation

I have a conceptual confusion about the metric moduli of Calabi-Yau manifolds, when I was reading Calabi-Yau compactification. As I understand, the metric moduli is parametrized by infinitesimal ...
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2answers
190 views

Mathematica package for supergravity and string theory [duplicate]

I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra ...
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Stability condition for AdS background (when gravity coupled to matter fields)

In finding the stability condition for AdS background (when gravity coupled to matter fields), why the conserved energy should be positive?
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Problems book recommendation on supersymmetry, supergravity and superstring theory

I'm learning supersymmetry, supergravity and superstring. I want some problems books to have some idea in this area. Is there this kind of books? Or are there some papers that have many solved model?
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Supergravity, torsion and diffeomorphism invariance

The action for $N=1$ supergravity in an $4$ spacetime dimenions is $$ S= \int e\left( R + \overline{\psi}_a \gamma^{abc} D_b \psi_c \right) $$ Here $R$ is the scalar curvature, $e=\det(e_{a\mu})$, ...
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Gauge invariance of Rarita-Schwinger action in curved spacetime

The Rarita-Schwinger action in curved $n$-dimensional spacetime is $$ \int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c $$ Here $g = \det(g_{\mu \nu})$, and the indices $a, b \dots$ are ...
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Do exact beta functions exist in (super)gravity theories and string theory?

An exact beta function exists for Super-Yang-Mills theories in 4D without matter - the so-called NSVZ beta function. Does a similar exact beta-function exist in gravity or supergravity theories? In ...
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71 views

Under what conditions is a vector-spinor gamma trace free

I came upon the concept of irreducible vector-spinors while trying to simplify an expression involving the gravitino field. It is claimed that an irredicible vector-spinor is gamma-traceless, i.e. $$ ...
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Does the covariant derivative of a derivative of the metric vanish?

The title holds the main question. For a little more backgroud: In a calculation I keep coming across terms of the form $$ D_M \partial_N e_P^A \overset{?}{=} 0$$ where $e_P^A$ is the vielbein and ...
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Kähler and complex manifolds

I was wondering if anyone knows any good references concerning Kähler manifolds and complex manifolds? I am studying supergravity theories and for the simplest $\mathcal{N}=1$ supergravity we will get ...
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Moduli Stabilization in 6D Einstein-Maxwell theory - Fluxes and O3 planes

I'd like to do the maths for the moduli stabilization of 6D Einstein-Maxwell Gravity $$ S= \int d^6X \sqrt{-G_6}(M_6^4R_6[G_6]-M_6^2|F_2|^2), $$ where the 6D metric is specified by $$ ds^2 = ...
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Betti multiplets in Kaluza Klein compactifications

It is well known that if the compactification manifold of a supergravity theory has non-zero Betti numbers, this may lead to the so called Betti multiplets in the spectrum of the low dimensional ...
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What's the Noether charge associated with Kaehler invariance of SuGra?

What is the Noether charge associated with Kahler invariance of supergravity (SUGRA)? As the question is rather tangential to what I need to do, I have not tried explicitly calculating it myself, but ...
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Is there an intuitive way of thinking about the extra dimensions in M-Theory?

Why are 11 dimensions needed in M-Theory? The four I know (three spatial ones plus time) have an intuitive meaning in everyday life. How can I think of the other seven? What is their nature (spatial, ...
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SuperConformal approach to SuperGravity

In the book (Supergravity - Daniel Z.Freedman & Antoine Van Proeyen - Cambridge), there are (Chapters 16-17) a presentation of pure supergravity or supergravity with matter, from a SuperConformal ...
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Obtaining supergravity from gauging global supersymmetry

On page 92, my still favorite supersymmetry book says, by making the global infinitisimal parameter of a SUSY tranformation spacetitime dependent (gauging) it forces one to introduce a new gauge field ...
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IIA and IIB Compact on 8D

How can compactifying IIA (non-Chiral) and IIB (Chiral) Superstring on $T^2$ (2-torus) gives rise to ($2$ dual descriptions of) the same $\mathcal N = 2$ supergravity in $8$ dimensions? I don't see ...
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What is on the AdS side in AdS/CFT supergravity or string theory?

What really is on the AdS side in AdS/CFT, does it always have to be string theory or is sometimes supergravity "enough" or better suited to do calculations? From the answers to my earlier question, ...
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Is it possible to derive the brane action in pure supergravity?

The branes that source the RR fields of supergravity are described by the DBI action plus a CS term. I know this only from superstring considerations. Is there a way to find this result without ...
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Bosonic-Fermionic interactions in supersymmetry

There are a lot of supersymmetric theories, and, sometimes,in the Lagrangian, there are interacting terms between bosonic and fermionic degrees of freedom, and sometimes not. Why ? For instance, for ...
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Construction of the supergravity side explicitly in gauge/gravity dualities

Although the motivation of this question comes from the AdS/CFT correspondence, it actually is related to a more general principle of gauge/gravity duality. We know from Maldacena's conjecture that a ...
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Can Divergences in Nonrenormalizable Theories Always Be Absorbed by (An Infinite Number of) Counterterms?

For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian: $\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$. In 8 ...
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Why does in string theory the amount of supersymmetry have to be $\cal{N} \leq 2 $?

Why is this, that in string theory the maximum amount of supersymmetry is $\cal{N} = 2$, whereas in supergravity one can have up to $\cal{N} = 8$ ?
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Supersymmetry calculations using computer algebra

Already the early papers on supergravity were written using computer algebra software to do some calculations. What modern packages do people normally use for doing such calculations? Of course ...
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Hybrid Inflation and Supergravity

Is it necessary to add a constant term in the superpotential of hybrid inflation within supergravity in order to cancel SUSY vacuum energy at the end of inflation?
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Divergence in Supergravity

I'm not familiar with supergravity so here's my question: I've heard in talks that if one finds divergence for five-loop 4-graviton scattering amplitudes in five dimensions this translates to a ...
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Boundary conditions in AdS/CFT

This question is in reference to this very famous paper of Witten. In general through the whole paper why is the author able to just focus on the scalar field propagating in the bulk and not need ...
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What is the generalization, if any, of the weak and dominant energy conditions to SUGRA?

In standard general relativity, we have the null energy condition, the weak energy condition related to stability, and the dominant energy condition related to forbidding superluminal causal ...
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Why doesn't the anthropic principle select for N=2 SUSY compactifications with an exactly zero cosmological constant?

The party line of the anthropic camp goes something like this. There are at least $10^{500}$ flux compactifications breaking SUSY out there with all sorts of values for the cosmological constant. Life ...