7
votes
Accepted
Why are there no branes in heterotic string theory?
The systematic way to deduce the brane content of string/M-theory is to classify the WZW-terms ($\kappa$-symmetry terms) for the would-be Green-Schwarz action functionals for the possible super $p$-...
- 13.7k
7
votes
Accepted
Supersymmetric background and fermion variations
Let me first describe the basic idea without even mentioning supergravity. Consider some classical field theory of two fields $\phi$ and $\sigma$, with an action $S[\phi,\sigma]$. Suppose this theory ...
- 1,273
7
votes
Accepted
What is a theory of gravity?
As an operational definition, a theory of gravity is a theory that reduces to the known working descriptions of gravity (Newtonian gravity, General Relativity) in some limit.
(If you think this is a ...
- 125k
7
votes
Accepted
Relationship between scaling dimension and mass in AdS/CFT
This is a bit long, but I'm going to be super precise.
Let's work in Poincare coordinates in AdS,
$$
ds^2 = \frac{L^2}{z^2} ( dz^2 + dx^\mu dx_\mu ) .
$$
$\Delta$ is the eigenvalue of scale ...
- 26k
6
votes
Action with self-dual field strength
Suppose you have a self-dual five-form field strength $F_5=*F_5$. The kinetic term of this field strength is proportional to
$$
\int F_5\wedge*F_5=\int F_5\wedge F_5=-\int F_5\wedge F_5
$$
where I ...
- 626
6
votes
Accepted
$E_{7(7)}$ symmetry in $(\mathcal{N}=8, d=4)$ Supergravity
1- Scalar fields generally involve a coset manifold structure $G/H$, the coordinates to which basically describe scalar fields as per some sigma model structure. The manifold describing scalar fields ...
- 787
5
votes
In what sense is gravity "gauge theory squared"?
I think I see the source of your confusion: when amplitudes people talk about gravity being gauge theory squared, we've already stripped off the gauge group.
You talk about eight $A_\mu^a$ in QCD. ...
- 198
5
votes
Accepted
Relationship between compactification moduli and generations in standard model
In general in such heterotic compactifications on a Calabi-Yau manifold $X$, you have a structure group $G$ whose commutant is the effective low-energy structure group $H$, and you get effective ...
- 125k
5
votes
Accepted
Why is 11 Dimensional SUGRA not a consistent quantum theory?
Essentially the answer is that the eleven dimensional supergravity is non-renormalizable; to be precise, above two loops, the graviton-graviton scattering amplitude is divergent. A nice review on the ...
- 3,852
5
votes
What is "string universality"?
The five consistent superstring theories are UV-complete and consistent quantum theories of gravity; that's demonstrably true. Adding M-theory (the eleven-dimensional supergravity) to that set of ...
- 3,852
4
votes
Problems book recommendation on supersymmetry, supergravity and superstring theory
For Supergravity, my recommendation is, without any doubt, the new edition (2015) of Gravity and Strings by Tomas Ortin. With more than 1000 pages, this book is an impressive piece of work on Gravity, ...
4
votes
Why torsion vanishes in supergravity?
In SUGRA, torsion does NOT vanish. You are always left with fermionic torsion terms. The spin connection includes torsion terms in SUGRA that does not vanish
$\omega_\mu{}^{a b} (e, \psi_\mu) = \...
- 724
4
votes
Accepted
Why is 11D supergravity part of M-theory?
The five superstring theories correspond uniquely to the five possible SUGRA theories in 10d as their low-energy effective theories.
The five SUGRA theories can be obtained by various styles of ...
- 125k
4
votes
Accepted
Question about Type IIB supergravity equations of motion
For a target space $p$-form in local coordinates
$$F_p~=~\frac{1}{p!}F_{\mu_1\mu_2\ldots\mu_p}~\mathrm{d}x^{\mu_1}\wedge \mathrm{d}x^{\mu_2}\wedge\ldots\wedge \mathrm{d}x^{\mu_p},\tag{1}$$
the ...
- 202k
4
votes
Accepted
Why the maximum number of supercharges in supergravity must be $Q=32$?
You have to first understand the contruction of massless multiplets which is found in the beginning of every introduction to supersymmetry, so I won't repeat it here. Then the argument goes like this:
...
- 627
4
votes
SUGRA & consistent field theories
Not sure what you mean by "belief". Composite spin 3/2 fields are permeating our world, viz the Δ(1232) baryon.
Fundamental Rarita-Schwinger (R-S) fields propagate acausally, as proven in a ...
- 62.8k
4
votes
Accepted
Is there a Lagrangian for Super-Gravity?
Consider the simple case of $\mathcal{N}=1$ on-shell supergravity in 4 dimensions with no matter content. The full action is made up of the Einstein-Hilbert term and the Rarita-Schwinger action for ...
- 8,445
4
votes
Accepted
Dimensional Reduction and Supersymmetry
The notation $\mathbf{n}$ for a number $n$ in the context of Lorentz representations denotes the dimensionality of this representation. E.g. denoting the Majorana representation of $\mathrm{SO}(10,1)$ ...
- 125k
4
votes
Accepted
Kaluza-Klein reducing the Chern-Simons term in 11D supergravity
$\newcommand{\d}{\mathrm{d}}\newcommand{\w}{\wedge}\newcommand{\R}{\mathbb{R}}$That integral vanishes because the differential form $\omega_i\w\omega_j\w\omega_k\in\Omega^6(S_4)$ vanishes (you cannot ...
- 4,559
3
votes
Question about Type IIB supergravity equations of motion
$F_{n-1}$'s are curvatures of higher gauge fields $A_{n-1}$'s, so they are n-forms. The expression $(F_{n}^2)_{\mu \nu}$ means schematically $F_{\mu \rho_1 \cdots \rho_{n-1}} F_{\nu}^{\phantom{a} \...
- 1,986
3
votes
Accepted
$\mathcal{N}=8$ Gauged supergravity from $d=11$ supergravity
$T^7$ is basically $S^1\times S^1\times...$ seven times and is just an extended version of compactification on $S^1$ where an abelian vector field gauges the U(1) isometry of $S^1$. In a general case ...
- 787
3
votes
Supergravity calculation using computer algebra system in early days
I don't know about this particular paper, but I do know that several early supergravity computations were checked using a computer algebra program 'Abra' written in Pascal by Mees de Roo. You could do ...
- 161
3
votes
Superconformal approach to supergravity
The "simplest" link, is NOT to begin with a Superconformal gauge multiplet coupled to a chiral multiplet, but to couple the Weyl multiplet to a superconformal chiral multiplet.
It is just a ...
- 724
3
votes
Accepted
Is there a simple way to understand why SUGRA is two-loop renormalisable?
This does seem to be the way that 2-loop finiteness of $\mathcal{N}=1$ SUGRA was discovered. A discussion of the construction of possible counterterms is given in e.g. this reference: [arXiv1506....
- 4,398
3
votes
What is meant by the coupling term $g_{\mu\nu}T^{\mu\nu}$ in Supergravity?
By "definition", the energy momentum tensor in GR is defined by the functional derivative.
$$ T^{\mu\nu} = \frac{\delta}{\delta g_{\mu\nu}}\mathcal{L}_{matter} $$
This "functional derivative ...
- 11.6k
3
votes
Accepted
Why are photons particles and waves, instead of particles that simply move in a wave pattern?
Photons are considered by most physicists to be neither waves nor particles, but to exhibit behaviours of both. In almost every experiment, they exhibit the behaviour associated with one or the other ...
- 84
3
votes
Why are photons particles and waves, instead of particles that simply move in a wave pattern?
The mainstream approach to quantum mechanics makes particle-like and wave-like characteristics just different manifestations of the same thing. Your approach is similar to Bohmian Mechanics, where the ...
- 1,227
3
votes
Accepted
Gauging $R$-Symmetry
Late answer, but the $U(1)$ R-symmetry cannot be gauged in global SUSY. This can be seen from the fact that it rotates the fermionic coordinates $\theta$, which are independent of spacetime ...
- 2,706
3
votes
Supergravity 3-form $C$ fields from 2d string worldsheets
I'm just going to consider the bosonic sector in the following. I think your issue comes from this:
the fundamental degrees of freedoms are from string worldsheets (so at most they are fundamentally ...
- 196
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