All Questions
Tagged with supersymmetry mp.mathematical-physics
18 questions
2
votes
0
answers
65
views
Link between Extended Supergauge Group and Twistor Theory
In a 1974 paper on supergauge transformations in four dimensions, Wess and Zumino considered an extended supergauge group which contains the conformal group as a subgroup. An interesting thing about ...
- 5,146
4
votes
0
answers
116
views
Superspace derivation of supersymmetric non-linear sigma model in Supersolutions by Deligne and Freed
I am having a little trouble understanding passage from the linear to the non-linear sigma model in Section 4.1 of Supersolutions by Deligne and Freed. Most of my confusion comes down to the ...
user482049
3
votes
1
answer
200
views
Supersymmetric SYK Model in 3D?
In a 2017 article More on supersymmetric and 2d analogs of the SYK model by Murugan, Stanford and Witten, the authors take a model called the SYK model (named after Sachdev, Ye and Kitaev) and study ...
- 5,146
13
votes
0
answers
992
views
What is a BPS state and why is it the cohomology of a moduli space?
The notion of a BPS state has existed in physics for a long time: I do not understand it completely, but I get the impression they are the supersymmetric analogue of ground states, and then physicists ...
- 5,701
7
votes
1
answer
265
views
Chain rule for the superderivative
A one dimensional complex supermanifold $X$ is locally described by an ordinary complex coordinate $z$ and an anticommuting coordinate $\theta$, $\theta^2 = 0$.
The superderivative is the square root ...
- 749
3
votes
1
answer
258
views
Supersymmetry charge $Q$ as anti-linear and anti-unitary operator
We know the supersymmetry (SUSY) charge $Q$ satisfies the following relation respect to fermion parity operator $(-1)^F$:
$$
(-1)^F Q + Q (-1)^F :=\{Q, (-1)^F \} =0
$$
which defines the anti-...
- 10.5k
6
votes
0
answers
221
views
References for superhomology
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("observables") of the weakly coupled topological string B-model on a Calabi-Yau ...
- 502
2
votes
1
answer
89
views
Sufficient conditions for unitarity of a representation of a Lie Superalgebra
Suppose we have a Lie superalgebra with triangular decomposition:
\begin{equation}
\mathfrak{g} = \mathfrak{g}^{+} \oplus \mathfrak{g}^{0} \oplus \mathfrak{g}^{-}
\end{equation}
I've seen it stated ...
- 61
11
votes
0
answers
600
views
The Grassmannian Gr(2,8) and an E7 surprise
Are there any mathematical explanations for the following surprising facts?
$$\int_{Gr(2,8)} c_{\text{top}}(TX(-2)) = 6556 = \frac{1}{2} \deg(E_7/P(\alpha_7)) + 1,$$
and
$$\int_{Gr(2,6)} c_{\text{top}}...
- 1,298
6
votes
1
answer
321
views
Branching from $E(6)$ to $SO(10) \times U(1)$
In $E(6)$ inspired models of supersymmetry, the inclusion of Lie subgroups
$$
SO(10) \times U(1) \hookrightarrow E_6
$$
is important object of interest. See here for my motivating example.
In ...
- 835
6
votes
1
answer
1k
views
Question on Witten’s paper “Supersymmetry and Morse theory”
EDIT. I am trying to read the article “Supersymmetry and Morse theory” by E. Witten (JDG 17 (1982)).
This well known article applies some tools developed by physicists (e.g. path integrals) to ...
- 21.8k
5
votes
0
answers
249
views
Localization principle in integration over supermanifolds
This post is closely related to the post Localization principle in supersymmetry
and can be considered as a continuation of it, although independent.
In § 9.3 of the book "Mirror symmetry" (K. Hori ...
- 21.8k
11
votes
4
answers
1k
views
Geometric or conceptual way to understand supersymmetry algebra
Is there any geometric or more direct conceptual way to understand a supersymmetry algebra, rather than starting from a Lagrangian including boson and fermion fields, deriving all the expressions ...
- 781
19
votes
7
answers
2k
views
Supermanifolds — elementary introduction?
I am looking for an elementary but mathematically precise introductory text on supermanifolds in a modern differential geometric setting.
Elementary in the sense that there is plenty of motivation for ...
- 3,873
8
votes
1
answer
405
views
How do you get the spectral curve from a Calabi-Yau?
In N=2 Quantum Field Theories and Their BPS Quivers by Alim, Cecotti, Córdova, Espahbodi, Rastogi and Vafa the authors give a recipe which constructs from a pair $(C,\phi)$ consisting of a Riemann ...
- 2,283
1
vote
2
answers
352
views
Witten index non-trivial in the context of Quantum Mechanics?
Let $H$ be a self-adjoint Hamiltonian and $H$ admits a decomposition into closed operators $D,D^*$, such that we have $H = D^*D$.
I will now consider the one-dimensional case on a compact set:
So ...
11
votes
1
answer
494
views
Is there a version of supersymmetry for homogeneous spaces?
The notion of "supersymmetry" that I am aware of proceeds as follows. One fixes a spacetime $\mathbb R^n$ and signature; I will write $\mathrm{SO}(n)$ for the corresponding group of orthogonal ...
- 54.6k
9
votes
1
answer
611
views
Matrix-tree theorem via supersymmetry (i.e. Grassman algebras)
The matrix-tree theorem states the number of spanning trees of a graph $G$ is equal to a modified determinant of the adjacency matrix or "graph Laplacian", $\Delta_G$:
$$\#\{ \text{spanning ...
- 22.8k