Aspects of the moduli space of instantons on $\mathbb{C}P^2$ and its orbifolds

Alessandro Pini; Diego Rodriguez-Gomez

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Aspects of the moduli space of instantons on $\mathbb{C}P^2$ and its orbifolds

High Energy Physics - Theory · Submitted 27 Feb 2015

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The authors' main claim Using this, we realize in $AdS_4/CFT_3$ (part of) the instanton moduli space providing at the same time further evidence supporting the $AdS_4/CFT_3$ duality.

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arXiv ID1502.07876 (version 2)

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CitationAlessandro Pini, Diego Rodriguez-Gomez. "Aspects of the moduli space of instantons on $\mathbb{C}P^2$ and its orbifolds." arXiv:1502.07876 (2015). https://pith.science/paper/RKOP5JQY

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We study the moduli space of self-dual instantons on $\mathbb{C}P^2$. These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact directions. In this paper we probe these, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover, the ADHM-like construction can be embedded into a $3d$ gauge theory with a known gravity dual. Using this, we realize in $AdS_4/CFT_3$ (part of) the instanton moduli space providing at the same time further evidence supporting the $AdS_4/CFT_3$ duality. Moreover, upon orbifolding, we provide the ADHM-like construction of instantons on $\mathbb{C}P^2/\mathbb{Z}_n$ as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on $\mathbb{C}^2/\mathbb{Z}_n$.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the moduli space of self-dual instantons on $\mathbb{C}P^2$.	contribution 0.88	0.87	0.04	asserted 0.95
s1	These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space.	method 0.77	0.27	0.04	asserted 1.00
s2	The latter has been found to be blind to certain compact directions.	gap 0.51	0.20	0.04	asserted 1.00
s3	In this paper we probe these, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings.	result 0.90	0.93	0.38	asserted 1.00
s4	Moreover, the ADHM-like construction can be embedded into a $3d$ gauge theory with a known gravity dual.	method 0.49	0.47	0.07	asserted 0.94
s5	Using this, we realize in $AdS_4/CFT_3$ (part of) the instanton moduli space providing at the same time further evidence supporting the $AdS_4/CFT_3$ duality.	interpretation 0.65	0.91	0.33	asserted 0.90
s6	Moreover, upon orbifolding, we provide the ADHM-like construction of instantons on $\mathbb{C}P^2/\mathbb{Z}_n$ as well as compute its Hilbert series.	contribution 0.97	0.95	0.10	asserted 1.00
s7	As in the unorbifolded case, these turn out to coincide with those for instantons on $\mathbb{C}^2/\mathbb{Z}_n$.	result 1.00	0.88	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.95.

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Original abstract

We study the moduli space of self-dual instantons on $\mathbb{C}P^2$. These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact directions. In this paper we probe these, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover, the ADHM-like construction can be embedded into a $3d$ gauge theory with a known gravity dual. Using this, we realize in $AdS_4/CFT_3$ (part of) the instanton moduli space providing at the same time further evidence supporting the $AdS_4/CFT_3$ duality. Moreover, upon orbifolding, we provide the ADHM-like construction of instantons on $\mathbb{C}P^2/\mathbb{Z}_n$ as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on $\mathbb{C}^2/\mathbb{Z}_n$.

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This is very similar to the case of instantons on $ℂP^2$ [ref] .

Towards Deconstruction of the Type D (2,0) Theory · Section · 0.91

What it cites · 69 sentences without a confident label

Uses the method or tool of 12 papers

The ADHM construction just introduced (and the corresponding orthogonal and symplectic versions in addition to their orbifoldings to be described below) allows to compute it using by now standard methods as in e.g. [ref] (see also [ref] for the study of instantons on $ℂ^2/Z_n$).

The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories · $U(N)$ instantons on $ℂP^2$ · 0.99
The ADHM construction just introduced (and the corresponding orthogonal and symplectic versions in addition to their orbifoldings to be described below) allows to compute it using by now standard methods as in e.g. [ref] (see also [ref] for the study of instantons on $ℂ^2/Z_n$).

The Hilbert Series of the One Instanton Moduli Space · $U(N)$ instantons on $ℂP^2$ · 0.99
The ADHM construction just introduced (and the corresponding orthogonal and symplectic versions in addition to their orbifoldings to be described below) allows to compute it using by now standard methods as in e.g. [ref] (see also [ref] for the study of instantons on $ℂ^2/Z_n$).

Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n · $U(N)$ instantons on $ℂP^2$ · 0.99

Compares with 3 papers

By explicit computation we find that the Hilbert series of the theory with gauge group $G=U(k_1) ×U(k_2) ×U(k_3)$ and flavor group $Sp(N_1) ×U(N_2)$ for the moduli space of instantons on $ℂP^2/ℤ_3$ coincides with the Hilbert series for the moduli space of $Sp(N)$ instantons on $ℂ^2/ℤ_3$ with gauge group $G=O(K_1)×U(K_2)$ and flavor groups $Sp(N_1) ×U(N_2)$ (see [ref] for more details) upon identifying [equation]

Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n · $Sp(N)$ instantons on $ℂP^2/ℤ_3$ · 0.86
In the particular case of $k_L=k_R$, upon setting $N=1$ and for $𝐤_L=𝐤_R=0$, the theory engineering the moduli space of unitary instantons on $ℂP^2$ becomes exactly that found in [ref] to describe M2 branes probing $𝒞×ℂ$, the direct product of a conifold times the complex line.

Chiral flavors and M2-branes at toric CY4 singularities · Rank one and AdS/CFT · 0.90
This is indeed analogous to the cases discussed in [ref] , where only the “closed string fields" in the quiver are captured by the gravity dual.

Probing the Higgs branch of 5d fixed point theories with dual giant gravitons in AdS(6) · Rank one and AdS/CFT · 0.81

Cites as support 4 papers

Nevertheless, as shown in [ref] (see also [ref] , and [ref] for a discussion in the physics context), the Hilbert series and other properties do indeed satisfy properties compatible with the expected hyperKähler condition of the moduli space.

Instanton counting on blowup. II. $K$-theoretic partition function · Introduction · 0.97
Nevertheless, as shown in [ref] (see also [ref] , and [ref] for a discussion in the physics context), the Hilbert series and other properties do indeed satisfy properties compatible with the expected hyperKähler condition of the moduli space.

Perverse coherent sheaves on blow-up. I. a quiver description · Introduction · 0.97
Nevertheless, as shown in [ref] (see also [ref] , and [ref] for a discussion in the physics context), the Hilbert series and other properties do indeed satisfy properties compatible with the expected hyperKähler condition of the moduli space.

The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories · Introduction · 0.97

Cites as background 4 papers

Indeed, as reviewed in [ref] following [ref] , we can characterize the instanton by its first Chern number $ĉ$ and its instanton number $k̂$.

Perverse coherent sheaves on blow-up. I. a quiver description · $U(N)$ instantons on $ℂP^2$ · 0.89
Indeed, as reviewed in [ref] following [ref] , we can characterize the instanton by its first Chern number $ĉ$ and its instanton number $k̂$.

The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories · $U(N)$ instantons on $ℂP^2$ · 0.89
We refer to [ref] and references therein for further explanations.

Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n · Constructing $Sp(N)$ instantons on $ℂP^2/ℤ_n$ · 0.95

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