A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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98
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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
46
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2k views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
15
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252 views

Is there any way to distinguish experimentally gauge mediation from gravity mediation in an unambiguous way?

There are lots of models of gravity mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental singnatures that could ...
11
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336 views

Apparent failure of SUSY nonrenormalization theorem

I am having trouble reconciling two pieces of information. Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, $h$ and $\hat{h}$. The ...
8
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143 views

Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
7
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186 views

What really are exotic supersymmetric black holes?

I have just read (in the black holes chapter 14 on p244 of this book Ref.1) that in string theory, when one adds an (electric?) charge $Q$ to a static black hole, one can arrive at an exotic ...
7
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153 views

How to perform contour integral in Nekrasov's formula

My question is technical. It is about instanton counting calculation (see this paper). The partition function of SU(N) gauge theory with $N_f$ fundamental multiplets in k instanton background is ...
6
votes
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231 views

Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
6
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271 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
6
votes
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150 views

Can pure-bosonic string theories exist in curved spacetime?

Question: Can there be a consistent non-supersymmetric pure-bosonic string theory in some curved spacetimes? Reason: Since fields with certain amount of negative mass can exist in curved spacetime ...
6
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118 views

Intuition for Homological Mirror Symmetry

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
6
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182 views

Questions regarding $D=4 $ ${\cal N}=4$ supersymmetric Yang-Mills

I have some questions regarding the $D=4 $ ${\cal N}=4$ super-Yang-Mills theory (the one with a really long action which can be acquired by compactifying the 10-dimensional ${\cal N}=1$ theory). I ...
6
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108 views

sigma model on $S^1 \times S^3$

In arXiv:1207.3497 - 4D partition function on $S^1 \times S^3$ and 2D Yang-Mills with nonzero area, Yuji Tachikawa explains the partition function for an 4d $\mathcal{N}=2$ sigma model on $S^3 \times ...
6
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127 views

R charge of the chiral multiplet in $2+1$ dimensions

These are two examples that I am puzzled by, One can see in this paper on page 16 that for ${\cal N} =2$ theory on $2+1$ the R-charge of the $\phi$ and the $\psi$ is determined to be $\frac{1}{2}$ ...
5
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67 views

Finite corrections to the Higgs mass in SUSY

I am worried here about specific supersymmetric scenarios in which an energy scale above the TeV is introduces. An example would be the Seesaw extension of the Minimal Supersymmetric Standard Model. ...
5
votes
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255 views

Book with solved examples and exercise problems for SUSY

I am learning supersymmetry right now. I am mostly following Bailin and Love. I try to connect all the steps from the book and complete the derivations in order to get comfortable with the ...
5
votes
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75 views

N=4 SYM in terms of N=1- SO(6) in the yukawa term

I'm trying to write N=4 SYM in terms of N=1 superfields. I have the lagrangian $$\mathcal{L}=\frac{1}{16 k} \int d^2 \sigma \text{Tr} \big[W^a W_a\big]+c.c+\int d^4\theta \text{Tr}\big[\bar{\Phi}^i ...
5
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113 views

Bosonic-Fermionic interactions in supersymmetry

There are a lot of supersymmetric theories, and, sometimes,in the Lagrangian, there are interacting terms between bosonic and fermionic degrees of freedom, and sometimes not. Why ? For instance, for ...
5
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174 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
5
votes
0answers
121 views

Are irrelevant terms in the Kahler potential always irrelevant, even at strong coupling?

I've been reading about the duality cascade in Strassler's TASI '03 lectures (hep-th/0505153). He reminds us of the non-renormalization theorem theorem for the superpotential so that the beta ...
5
votes
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223 views

The ${\cal N} = 3$ Chern-Simons matter lagrangian

This question is sort of a continuation of this previous question of mine. I would like to know of some further details about the Lagrangian discussed in this paper in equation 2.8 (page 7) and in ...
5
votes
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96 views

Defects in 3+1 TFTs/2+1 CFTs

I would like to know of good pedagogic references to learn about the notion of "defects" in TFTs and CFTs. I am specially interested in 3+1 TFTs (.and probably about their relation to 2+1 CFTs..) In ...
4
votes
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73 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
4
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114 views

Pole in reflection/transmission coefficient and bound states

I was working on a scattering problem in a quantum mechanical system with Hamiltonian $$H_1=A^{\dagger}A=(-\partial_x+W(x))((\partial_x+W(x))).$$ One can show that a 'supersymmetric' partner to this ...
4
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56 views

Concerning topology of BPS states of the M5-brane

My question is about the M5-brane in M-theory. I would like to know whether the BPS states of the M5-brane worldvolume theory (especially the 1/2 BPS and 1/4 BPS ones) are independent of the topology ...
4
votes
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70 views

Why the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,1) \times U(1)_R$?

Why in $d=4$ $\mathcal{N}=1$ SCFT the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,1) \times U(1)_R$? More generally how can I determine the such a thing in other theories? Is there ...
4
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0answers
103 views

What decides the signs and coefficients of terms in superfield?

I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
4
votes
0answers
106 views

How do messenger fields break SUSY in the MSSM?

I have been reading the notes on Supersymmetry by Martin. I am trying to understand gauge mediated symmetry breaking. From what I understand, there is a hidden sector where SUSY is spontaneously ...
4
votes
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117 views

String theory and space-time supersymmetry

I actually want to know whether space-time supersymmetry is important for string theory consistency? I see that NS and GS supersymmetric strings have worldsheet supersymmetry, but the first one does ...
4
votes
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44 views

$\mathcal{N}=2$ spin $1/2$ supermultiplet

In Freedman and Van Proeyen's Supergravity, in the footnote on pg. 128, they say There is a subtle hermiticity requirement for $\mathcal{N}=2$, which requires the multiplet $(-1/2,0,0,1/2)$ must ...
4
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133 views

Coleman-Mandula theorem in mathematical language

Every supersymmetry text starts off mentioning the Coleman-Mandula theorem. Often it is introduced using rather colloquial terminology. I was wondering if anyone knew a precise mathematical ...
4
votes
0answers
101 views

Degrees of freedom in m(atrix) theory

The Hamiltonian for m(atrix) theory is given by $$H=\frac{1}{2\lambda}\text{Tr}\left(P^{a}P_{a}+\frac{1}{2}\left[X^{a},X^{b}\right]^{2}+\theta^{T}\gamma_{a}\left[X^{a},\theta\right]\right).$$ Where ...
4
votes
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93 views

Do commutation relations exist between superfields?

To quantize a theory, Klein gordon field for example, commutation relations are stablished. Or anticommuting ones in the fermionic case. If I have the Wess.Zumino model or the free model: ...
4
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69 views

Does the number of left handed chiral quark superfields always equal half the number of quark flavours?

In Weinberg's "The Quantum Theory of Fields Vol III" page 267 we're told that $n_f = 2N_f$. Where $n_f$ are the number of flavours and $N_f$ is the number of left chiral quark superfields (or the ...
3
votes
0answers
27 views

D-branes conserving only half of the supersymmetries

Concerning D-branes as BPS states from T-duality. In D-Branes by Johnson (and other sources) I find the following statement (p.196): "Only the total [supersymmetric] charge of $Q_a+\tilde{Q}_a$ of ...
3
votes
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33 views

Has anyone studied anomalous supersymmetry?

In this paper (and others), the authors study a supersymmetric model where the supercharge suffers an ABJ anomaly. Has anyone studied a supersymmetry with a 't Hooft anomaly (gauging the ...
3
votes
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62 views

How do I obtain the SUSY Transformations from Poisson Brackets?

In Friedman's and Van Proyen's Supergravity textbook it is explained how one can get the supersymmetry transformations using the conserved currents. Specifically this is in section 6 where we are ...
3
votes
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18 views

How does one determine the genus of the ultraviolet curve from Seiberg-Witten curve?

In Gaiotto's construction of 4d ${\cal N}=2$ theories, one starts with 6d (2,0) theory and compactify it on the Riemann surface, which is called the ultraviolet curve of the ${\cal N}=2$ theory. In ...
3
votes
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28 views

Baryonic operators in ${\cal N}=1$ $U(N)$ SQCD in four dimensions

Seiberg's duality is usually considered as a duality for $SU(N_c)$ theories with $N_f$ flavors. In his case, the vacuum for $N_f \geq N_c$ is parameterized by mesons $M$ and baryons ${\bar B}$ and ...
3
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83 views

Projective superspace: why extra bosonic coordinates

I'm studying the projective superspace formalism for N = 4 supersymmetric $\sigma$-models in two dimensions. My question is: why do we need the extra bosonic coordinates for the manifest action? I ...
3
votes
0answers
77 views

A question about genus one string amplitude

In BCOV's paper http://arxiv.org/abs/hep-th/9309140 the genus one string amplitude of a Calabi-Yau 3-fold was explained in the B-model as the Ray-Singer torsion (there is a similar discussion in the ...
3
votes
0answers
74 views

Meaning of the Coulomb and Higgs branch for non-Lagrangian theories?

What is the meaning of the Coulomb and Higgs branch for non-Lagrangian theories like the $T_N$ theories that arise as 5-brane webs and correspond to CY 3-folds in M-theory? This is related to an older ...
3
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74 views

Questions about the existence of 5d & 6d version of 4d ${\cal N}=2$ SCFTs

Given a 4d N=2 Superconfomal field theory (SCFT) with a global flavor symmetry ( $\mathfrak{f}$ as the corresponding lie algebra), can we clam that this theory can always flow from a 5d ${\cal N}=1$ ...
3
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58 views

What information do quiver gauge diagrams provide?

I am struggling to understand what the information one can extract by looking a quiver diagram for a quiver gauge theory is. I understand what quivers are but I cannot get some physical intuition and ...
3
votes
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61 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
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54 views

Spin of an operator in supersymmetric theories

How exactly is the spin of an operator in the context of a supersymmetric theory defined? For example, in page 25 of [1], $\mathcal{N} = 2$ supersymmetry is defined to have operators $J, G^{+}, G^{-}, ...
3
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89 views

New Supersymmetry Algebra

We know that SUSY generators commute with translation $$ [P_\mu,Q_\alpha]=0 $$ I have some questions: What is this equation physical meaning? Is it possible to make "SUSY-like" generators that do ...
3
votes
0answers
66 views

Highest weight unitary representations of $psl(2|2)$

I'm having some trouble understanding how to extend representation theory from Lie algebras to super Lie algebras, in particular with $psl(2|2)$. Ultimately I'm interested in 2D quantum sigma models ...
3
votes
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135 views

N=4 SYM from Klebanov-Witten field theory

This is with reference to M. J. Strassler's lectures on "The Duality Cascade" pg. 46. I want to see how $\mathcal{N}=4$ SYM emerges when D3 branes, in the KW setup, are placed at smooth point of the ...
3
votes
0answers
86 views

Cosmological constant (positive, dS) as SUSY/supertring issue

The "almost" de Sitter expansion of current cosmological model implies a puzzle for supersymmetry (SUSY) and also for string theory. A positive value of the cosmological constant implies a non-null ...