Questions tagged [moduli]
The moduli tag has no usage guidance.
26 questions with no upvoted or accepted answers
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Coulomb Branch vs. Higgs Branch (and the connection with D-branes, AdS/CFT)
I am confused about the difference between the Coulomb and Higgs branches of the moduli space of supersymmetric gauge theories. It's easy to find a definition for $D=4$, $\mathcal{N}=2$ supersymmetric ...
- 3,997
6
votes
0
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144
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Target space of boundary CFT dual to a bulk string theory ($AdS_3/CFT_2$)
I was reading the Maldacena Ooguri paper where they mention that for the string theory living on $AdS_3\times S_3 \times M_4$ (where $M_4$ is $K3$ or $T^4$), the boundary CFT is the supersymmetric ...
- 672
5
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204
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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
5
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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
5
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135
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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
4
votes
0
answers
112
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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
4
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0
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Moduli space for Riemann surfaces with boundaries and open string loop diagrams
I'm searching for information on the moduli space for Riemann surfaces with boundaries, like the ones used to compute open string loop diagrams. I found a huge lot of info for the case without ...
- 1,176
4
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0
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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
3
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0
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251
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Are Instantons Quantum or Classical?
I'm talking specifically about instantons on four-manifolds, but my confusion here is probably of a more general nature. So I'd also appreciate less specific answers!
Okay, so I know that in physics,...
- 697
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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 ...
3
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0
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65
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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
2
votes
0
answers
61
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Distance conjecture being false in $\phi^4$ theory
One part of Distance conjecture states that free theory (Higher spin) are at infinite distance away from any arbitrary point on conformal manifold where the distance is measured with respect to ...
- 3,063
2
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0
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322
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Vacuum manifold and moduli space
Vacuum manifold is just another name for the manifold spanned by the ground states of quantum field theory. It is also called moduli space.
According to https://en.wikipedia.org/wiki/Vacuum_manifold, ...
- 4,376
2
votes
0
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208
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What exactly do the zero-modes of the instanton mean?
I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
- 733
2
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0
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321
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Complexified Kahler moduli
The fundamental domain of the complex moduli of a torus can be identified to the upper half plane up to $SL(2,Z)$ transformations $\mathbb{H}/{SL(2,\mathbb{Z})}$, but I don't know why the complexified ...
- 49
2
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204
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Positivity of Bulk modulus and shear modulus in isotropic materials
I have been searching through many resources, but could not find a proper thermodynamic reasoning for why bulk and shear moduli for isotropic materials should be positive. Some resources like eFunda
...
- 131
2
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0
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245
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High Young's Modulus and Tensile Strength of Carbon Nanotubes
I was recently reading about Carbon Nanotubes having extremely high Young's moduli, as well as high Tensile Strength, making them very interesting fibers. However, when I read this I wondered what was ...
- 21
2
votes
0
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78
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Moduli potential in Type IIB String Theory
In the book String Theory and M-Theory by K. Becker, M. Becker and J.H. Schwarz:
Why is the potential for moduli given by eq (10.168):
$$\tag{10.168 }V(T,K) ~=~ \frac1{4\mathcal{V}^3} \Big( \int_{...
- 475
1
vote
1
answer
177
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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
1
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0
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Vacuum manifold and fermion condensation
Vacuum manifold is just another name for the manifold spanned by the ground states of quantum field theory. It is also called moduli space.
According to https://en.wikipedia.org/wiki/Vacuum_manifold, ...
- 4,376
1
vote
0
answers
72
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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
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0
answers
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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
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0
answers
231
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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
0
answers
152
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Tadpole-free condition
Tadpole-free is a very important condition for perturbative string theory (which is equivalent to the theory to be expanded around the "right" vacuum). For simplicity, let's consider closed string ...
- 651
0
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1
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163
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Holomorphic 3-form on Calabi-Yau compactifications
What is the natural scale of the holomorphic 3-form on a Calabi-Yau?
$\Omega=\frac{1}{3!}\Omega_{abc} ~ dz^a\wedge dz^b \wedge dz^c$
$||\Omega||^2 = \frac{1}{3!}\Omega_{abc}\bar{\Omega}^{abc}$
...
- 1
0
votes
0
answers
217
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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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