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

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Action with self-dual field strength

It is said that writing down an action in presence of a self-dual field strength is subtle and not known till date. The familiar example people give is that of type IIB super-gravity which has a ...
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Superconformal description of supergravity action

I've been reading this paper http://arxiv.org/abs/hep-th/0110263. In section 4, he discusses the benefits of writing the supergravity action in a superconformal way. I have a few questions regarding ...
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Problems with covariant action of the superstring

I was reading Kiritsis notes (http://arxiv.org/abs/hep-th/9709062), at page 105/106 (equation 10.1), where he has a covariant action of the superstring including the gravitino. I have problems showing ...
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Why torsion vanishes in supergravity?

Why is it (more often than not) considered in supergravity that the torsion vanishes in Cartan's first structure equation? What does the vanishing of the torsion imply?
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Decomposing massless N=8 SUGRA multiplet into multiplets of massless N=4

The only massless $N=8$ SUGRA multiplet is given by $(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$ where the greek upper ...
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Why are only certain fluxes allowed in 11D SUGRA?

In Type IIA/IIB string theory we can have various fluxes, such as the 3-form H-flux, and the various Ramond-Ramond fluxes in even/odd dimensions. In 11D SUGRA, however, the field content seems to ...
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Geometry of spacetime and spinor bilinears

In this paper (http://arxiv.org/abs/0704.0247) p.20, the author says in the section titled Geometry of spacetime the following: In order to obtain the spacetime geometry, we consider the spinor ...
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Killing vector and one-form [closed]

p. 21 in this paper (http://arxiv.org/abs/0704.0247) $V$ is Killing vector, where $V^2 = −4b\bar{b}$, which means it is timelike Killing vector. The authors say: From $V^2 = −4|b|^2$ and $V = ...
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How do we know if a Killing Spinor is Time-like or Null?

How to know whether a Killing spinor orbit is time-like or null? This is present in a paper like this 29/39 here. I'm not asking for a technical answer, just a logical cliche answer chit-chat answer. ...
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Basic Dirac Spinors question

Here p. 25, it says Generically, the space of Dirac spinors has $2^{d/2}$ (complex) components, and one can recast them in terms of the complexified space of forms on $\mathbb{R}^{d/2}$. My ...
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Brane interactions?

In particle physics, in QFT's, interactions come from the interaction piece in the Lagrangian (action). In string theory, waiting for a complete formulation of SFT, we have to add "by hand" ...
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What does $δF=0$ imply?

Please have a look here section 12.6. It says here that Given the action of a supergravity theory, it is generally useful to search for solutions of the classical equations of motion. It is ...
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What are susy transformations for N=2 sugra?

Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories. As suggested by some books and papers on ...
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I do not understand this comparison?

It is frequently discussed that to find solutions having some sort of supersymmetry is easier than solving Einstein’s equations of motion. I do not understand this discussion though. Specifically, ...
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Why supergravity is extension of GR?

Why is it that supergravity is an extension to general relativity? In what ways? What I have read until now says the following: GR got itself concerned with gravity after the revolution of special ...
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Why is the formulation of M(embrane) theory so hard? [duplicate]

The formulation of String theory is fairly straight forward in that the action is just the world-sheet area of a string. Then you can add supersymmetry in various ways. Finally you add some ghosts to ...
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How to visualize a sphere bundle?

In the paper ``Gravitational Anomaly Cancellation for M Theory Fivebranes", the authors consider removing a tubular region of radius $\epsilon$ around the M5 brane (in order to make sense of the three ...
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Local Lorentz transformations

If $\gamma^m$ denotes a tangent space gamma matrix, and $\gamma^\mu$ denotes a curved space gamma matrix, then they are related by $$\gamma^\mu(x) = \gamma^m e_{m}^{\mu}(x)$$ where $e_{m}^{\mu}(x)$ ...
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Could the gauged six-dimensional chiral supergravity model explain dark matter, as well as gravity?

I was reading a paper on 6-dimensional supergravity http://www.math.ist.utl.pt/~strings/MTST2/audio/pope1.pdf after watching a sixty symbols video on it https://www.youtube.com/watch?v=O4eXU8VHM2g ...
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What does naturally mean here?

We often cross the sentence "Kahler geometry emerges naturally in sugra". I have always wondered what does this mean; actually what does naturally mean in that sentence?
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Supersymmetry breaking and normalizable zero modes

Why does supersymmetry always lead to normalizable zero modes? For example, it is stated in the paper by Michelson and Kaplan (http://arxiv.org/abs/hep-th/9510053) that we can assume, without loss of ...
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Is M-Theory and 11D Supergravity the same thing?

Is M-Theory and 11D Supergravity the same thing? Reading Hawking, he uses 11D Supergravity and M-Theory interchangeably. ...
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Question about Supermatrix algebra

This question is inspired from a reading of Appendix F of P. van Nieuwenhuizen, Supergravity, Phys. Rep. 68 (1981) pp. 369-374. Consider a "supermatrix" $$M = \left(\begin{array}{cc} A & B\\ C ...
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Global symmetries in type IIB string theory vs type IIB supergravity

In the AdS/CFT correspondence I know that the mapping of global symmetries involves also the S duality that in the field theory side is $SL(2,Z)$. In Type IIB supegravity this duality is $SL(2,R)$. I ...
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New definition of gamma matrices?

It was mentioned in http://kclpure.kcl.ac.uk/portal/files/12371620/Studentthesis-Mehmet_Akyol_2013.pdf page 28, a new concept "oscillator basis" or more precisely the author defines gamma matrices of ...
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What causes gravity in M-Theory?

New and updated, because people were misunderstanding what I meant! General relativity describes gravity as the result of....(very roughly) spacetime curvature Newtonian gravity describes gravity as ...
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What is the Origin and physical meaning of R- multiplet and S-multiplet in Sugra?

In this summer, i learnt about various muliplet in Supergravity. First i summarize what i learn from the school. (i) Ferrar-Zumino multiplet The super-current multiplet satisfies \begin{align} ...
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Canonical spinors from gauge transformations

In this 2006 paper, http://arxiv.org/abs/hep-th/0610128, there is the concept of gauge transformation and how was it employed that I do not fully understand. Note, what will be talked about below is ...
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Elementary question about distributive property of variation operator on an exterior product

I am trying to work out the equations of motion of a 11-dimensional supergravity action $$S = \frac{1}{2\kappa^2}\left(\gamma\int d^{11}x\sqrt{|g|}\mathcal{R} - \frac{\alpha}{2}\int G \wedge \star G ...
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What is the definition of the duality group $E_{7(7)}$?

What is the definition of the duality group $E_{7(7)}$ that appears in ${\cal N}=8$ Supergravity and what are the basics properties? Moreover what is the relation with the Lie Algebra $E_7$? ...
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Instantons and Fivebranes

What is the general relationship between instantons and fivebranes? In the paper ``Magnetic Monopoles in String Theory'' by Gauntlett, Harvey and Liu, the authors state the fivebrane ansatz of ...
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Effect of orbifolding on form ields

A paper by Lalak et al, entitled "Soliton Solutions of M-theory on an orbifold", considers the brane solutions of 11 dimensional supergravity on a space of the form $R^{10} \times S^1/\mathbb{Z}_2$. ...
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Why are there no branes in heterotic string theory?

Why does the heterotic string (or heterotic supergravity) have no brane solutions? According to David Tong's notes: the heterotic string doesn’t have (finite energy) D-branes. This is due to an ...
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What happens to M2 and M5 brane solutions upon orbifolding?

M-theory has M2 and M5 brane solutions. Suppose M-theory is compactified on $\mathbb{R}^{10} \times S^{1}/\mathbb{Z}_2$, what happens to the M2 and M5 brane solutions? How does one define the near ...
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Can Bosons couple to gravity? Why do we need vielbein?

It is said that In theories such as Supergravity where there are fermions coupled to gravity, one must use an auxiliary quantity, the frame field (vielbein). In supergravity, can a boson be coupled ...
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Dirac Matrix property suitable to finding sets of intersecting branes

So, 11 dimensional supergravity has four oft-studied half-BPS states, the KK1 plane wave, the M2 brane, the M5 brane and the KK6 monopole. To figure out if we can find more solutions in the form of ...
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Kähler Potential of Calabi-Yau volume

At tree level, the Kähler potential is given by (neglecting complex structure) $K = -\ln(-\mathrm{i}(\tau - \bar{\tau})) - 2\ln(V_{CY})$ where $V_{CY} = \frac{1}{6} \kappa_{abc}t^at^bt^c$ ia the the ...
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Local translations in curved spacetime

A global Poincare transformation on a scalar field induces $$\delta(a, \lambda)\phi(x) = [a^{\mu}+\lambda^{\mu\nu}x_{\nu}]\partial_{\mu}\phi(x). \tag{11.46}$$ In curved spacetime we replace $a^{\mu} ...
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From String Frame to Einstein Frame for 10D supergravity

This question is related to but not answered in the post String frame and Einstein frame for a Dp-brane, so it should be treated as a separate question. Beginning with the gravity action $$S = ...
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Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - ...
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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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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 ...