All Questions
Tagged with moduli supersymmetry
18 questions
5
votes
0
answers
204
views
Modified Special Geometry of SUSY Moduli Space
It is known that the Coulomb branches of 5d $\mathcal{N}=1$ and 4d $\mathcal{N}=2$
SUSY (both have eight supercharges) satisfy special geometry. This means that there exists a holomorphic prepotential ...
- 57
1
vote
1
answer
177
views
Dimension of moduli space for SQCD
We are in $\mathcal{N}=1$ SUSY. Consider massless SQCD with gauge group $SU(N)$ and $F$ flavours. The quarks superfields $Q$ and $\tilde{Q}$ are $F\times N$ and $N\times F$ matrices respectively and ...
- 101
4
votes
0
answers
112
views
Parametrization of classical moduli space for SUSY QED
A bit of context
I'm following Bertolini's notes on SUSY and in section 5.3.1 he claims that, for a SUSY theory without superpotential, i.e. in which the $D$-flat directions coincides with the moduli ...
- 101
5
votes
0
answers
187
views
Difference between moduli spaces of supersymmetric vs non-supersymmetric theories?
I have a basic conceptual question regarding the difference between moduli spaces in supersymmetric vs non-supersymmetric theories.
In usual non-supersymmetric theories, the existence of flat ...
- 163
1
vote
0
answers
72
views
Describing Calabi–Yau 3-fold
Background:
In Calabi-Yau 3-fold, the Kähler metric is given in terms of the Kähler potential $\kappa$ :
$ g_{i\bar{j}} = \partial_i \partial_{\bar{j}} \kappa$,
where $i, \bar{j}$ = 1,2,3 $ ( the ...
- 405
1
vote
0
answers
23
views
Checking modularity-like transformation property
Assume $M$ is a 4 manifold. Let $Z_v$ be partition function of fixed magnetic flux $v$ with all instanton configuration summed over where $v\in H^2(M,Z/nZ)$. $\tau$ denotes complex parameter on upper ...
- 411
1
vote
0
answers
231
views
Relation between the momentum map and D-terms
Can someone explain to me the relation between the momentum map linked to symplectic quotients and the D-terms of a scalar potential for a $\mathcal{N}\geq 2$ supersymmetric gauge theory?
I am ...
1
vote
1
answer
1k
views
Higgs and Coulomb Branches. What are they?
On Wikipedia, there is an article on Moduli(Physics). The link is the following https://en.wikipedia.org/wiki/Moduli_(physics) . What captures me is Higgs and Coulomb Branch. If you click the links on ...
user151266
3
votes
1
answer
777
views
Why is important to know the geometry of the moduli space of vacua in a SUSY gauge theory?
I'm studying the moduli space of vacua for some supersymmetric gauge theory and I want to know specifically why it is important to know the geometry of this space. I know everything about the division ...
5
votes
0
answers
135
views
Flux compactifications and the scalar potential
Does the scalar potential:
$$V=e^K(K^{I \bar{J}})D_IW D_{\bar{J}}\bar{W}-3|W|^2$$
where $K$ is the Kähler potential and $W$ the superpotential, $D=\partial_I+\partial_IK$ and $I$ runs over all the ...
- 205
5
votes
1
answer
926
views
Moduli spaces of supersymmetric field theories and their singularities
I'm a mathematician doing some work which is related to $\mathcal N=2$ supersymmetric quantum field theory in $d=4$ and am a little confused about the physical notion of moduli space in this context. ...
- 151
7
votes
2
answers
267
views
Flavor symmetry fixes the Higgs branch in any 4D ${\cal N}=2$ QFT
Let us consider two different quantum field theories in 4 dimensional Minkowski spacetime, call them theory A and theory B, with 8 supercharges.
(i.e. 4D $\mathcal{N}=2$ theories). Let $G_A$ be the ...
- 2,241
0
votes
0
answers
217
views
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 ...
- 142
4
votes
0
answers
100
views
Moduli space for $CP^N$ and $T^{*} CP^N$ in $\mathcal{N}=2$ SUSY
For complex $\phi$ in $U(1)$ gauge theory,
\begin{align}
|\phi_1|^2 + |\phi_2|^2 +\cdots |\phi_N|^2 =r
\end{align}
This equation $|\phi|^2=r$, describes sphere $S^{2N-1}$. Dividing the space of this ...
- 3,662
0
votes
1
answer
1k
views
Higgs branch and Coulomb branch
I heard that the distinguish between Higgs branch and Coulomb branch is the limit of some parameters. (If i remember correctly, something like FI parameters. )
Here i want to know what is FI ...
- 3,662
8
votes
1
answer
1k
views
What's the Coulomb Branch and why is it important?
I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the ...
- 105
9
votes
1
answer
703
views
What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?
When reading about Higgs and Coulomb 'phases' I came across two separate definitions:
The first tells us that the Higgs/Coulomb phases are determined by the representation that the Higgs field ...
- 1,998
3
votes
0
answers
65
views
Linear combination of anomalous dimensions in effective potential on pseudomoduli space
In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3).
In this equation, ...
- 341