Questions tagged [moduli]
67 questions
18
votes
1 answer
Instanton Moduli Space with a Surface Operator
I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator.
Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are isomorphic.
the moduli space of ASD connections…
Satoshi Nawata
15
votes
2 answers
Is the partition function of non-conformal theories on a torus modular invariant?
Usually we say that the partition function of CFTs on a torus is modular invariant, because we define theory on a torus. If I have a non-conformal field the theory on a torus, is its partition function still modular invariant?
Nahc
- 2,161
13
votes
1 answer
What is the Moduli Space, and why do we care about it?
What is the moduli space of a QFT?
What does it mean exactly that there are different inequivalent vacua?
Can someone give a precise definition of the moduli space, and some easy examples?
And why is it so important and studied nowadays?
Federico Carta
- 2,261
10
votes
1 answer
precise definition of "moduli space"
I'm curious what the precise definition of the moduli space of a QFT is. One often talks about the classical moduli space, which then can get quantum corrections. Does this mean the quantum moduli space is something like the set of minima of the…
user6013
- 943
10
votes
1 answer
How can I understand instantons as sheaves?
In specific, instantons are considered or interpeted as torsion free coherent sheaves. Why is that the case? Is there a nice way to understand this relation and of course also understand how the two moduli spaces (instantons and torsion free…
Marion
- 2,238
10
votes
0 answers
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 field theories: The moduli space is locally a…
Surgical Commander
- 4,057
9
votes
1 answer
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 transforms under, as explained on Wikipedia. The Higgs…
Siraj R Khan
- 2,028
8
votes
1 answer
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 concept but I always find very long and complex…
miguelFe
- 105
7
votes
2 answers
Why should bulk modulus always be positive?
The minus sign that appears in Equation 12.39 is for consistency, to ensure that $B$ is a positive quantity. Note that the minus sign ($–$) is necessary because an increase $\Delta p$ in pressure (a positive quantity) always causes a decrease…
Nitish
- 87
- 6
7
votes
1 answer
Disappearance of moduli for condensate of open strings
Consider a Dp-brane. Compactify $d$ spatial dimensions over a torus $T^d$. Suppose $d\geqslant p$, and that the Dp-brane is completely wrapped around the compactified dimensions.
Look at the open string modes ending on this wrapped D-brane. There is…
Hecles
- 71
7
votes
2 answers
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 flavor symmetry group of A, and $G_B$ the flavor…
Federico Carta
- 2,261
6
votes
1 answer
Background Gauge Condition In Moduli Space
I'm really confused on the background gauge condition for the moduli space of BPS-monopoles:
\begin{equation}
D_i \delta A_i + e [\phi , \delta \phi]=0
\end{equation}
I can see that this conditions is the same as saying that $\delta A_i$, $\delta…
Hunter
- 5,328
6
votes
0 answers
Target space of boundary CFT dual to a bulk string theory ($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 sigma model whose target space is the moduli space…
Michael Williams
- 672
6
votes
1 answer
Multiple vacua vs. VEVs in QFT
Take a (possibly supersymmetric) relativistic quantum field theory:
when we construct it, we suppose that there is a unique vacuum state $|0\rangle$ which is Lorentz invariant, vector of some Hilbert space and annihilated by all annihilation…
jj_p
- 1,254
6
votes
1 answer
Poisson structure on moduli space of CFTs
The moduli space of CFTs with central charge 26 forms the classical phase space of bosonic string theory, in some sense. Similarily the moduli space of SCFTs with central charge 10 forms the classical phase space of type II superstring theory
We…
Squark