Quantum Mirror Map for Del Pezzo Geometries
Yuji Sugimoto
(Univ. of Science and Technology of China)
with Sanefumi Moriyama Tomohiro Furukawa
Quantum Mirror Map for Del Pezzo Geometries Yuji Sugimoto (Univ. - - PowerPoint PPT Presentation
Quantum Mirror Map for Del Pezzo Geometries Yuji Sugimoto (Univ. of Science and Technology of China) with Sanefumi Moriyama Tomohiro Furukawa (Osaka City Univ.) arXiv:190?.????? Susy. Gauge Theory encoded in algebraic curve Mirror Map
(Univ. of Science and Technology of China)
with Sanefumi Moriyama Tomohiro Furukawa
Free energy relating to BPS indices
ΠA(z) ∼ c1z + c2z + ...
<latexit sha1_base64="v525ikpCJY0awz2BguTKZ9/oYU=">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</latexit>ΠA(z) ∼ c1z + c2z + ...
<latexit sha1_base64="v525ikpCJY0awz2BguTKZ9/oYU=">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</latexit>(see also Moriyama, Kubo, Furukawa’s slides&Poster)
b H = ⇣ b Q1/2 + b Q−1/2⌘ ⇣ b P 1/2 + b P −1/2⌘
<latexit sha1_base64="AJRuSImHKoCnLtYIHOG/XNRLmvY=">AC+nichZHLSsNAFIZP4v3aqhvBTbAoilgnVAEQXDjshfrBaslSaft0DQJybSlxryAL+DClYILcSu+gBtfwIULH0BcKrhx4WkaFOvthGTO/HO+k384qUzhxNyL4ht7R2dXd09vX39A4Oh8NDwpmNWbI2mNVM37W1VcajODJrmjOt027KpUlZ1uqW1hrnW1VqO8w0NnjdontlpWCwPNMUjlI2XMvUWI4WFe6ue9KlNFpnk9aAlv35XnYp40I3RZn0xY7NCkU+3QvEfoHgrlA1HSJT4IX1P5CJQBxM3wNGciBCRpUoAwUDOCY6CAg8uyEDAQm0PXNRszJh/TsGDXmQrWEWxQkG1hN8C7nYD1cB9o6fj0xr+RcfXRlKCXJHLsgzuSWX5JG8/drL9Xs0vNRxVZstbKho9HU679UGVcOxU/qT8c8rDke2Xo3fKVxi20Jl89OH5OLScn3ElyRp7Q/ym5Jzd4A6P6op0naPLkDz8qevFwPHLrML4nm7GoPB+NJRYiqzvBoLphDMZhCqexCKuwDnFIY/cHoU3oFwbEQ/FMvBAvm6WiEDAj8CXEq3chPrtK</latexit>[Aharony-Bergman-Jafferis-Maldacena 2008]
b Q b P = q b P b Q
<latexit sha1_base64="9xBWkbLZxOgSEDpiWJNTaNKejU=">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</latexit>b H = h⇣ Q1/2 + Q−1/2⌘ ⇣ P 1/2 + P −1/2⌘i2
<latexit sha1_base64="/h01glb193CpEtEnr7M8lsf9ZLU=">ACv3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQtExZRnpqRmJZUe9Ry2cbkpKaVRCuAKY3AuGpDfaNabSCtC2IoxBRlpmeUaEKlA6DSAWjSECo2ziheQNlAzwAMFDAZhlCGMgMUBOQLGeIYUhyGdIZihlyGVIZchjKAGycxgSGYqBMJrBkMGAoQAoFstQDRQrArIywfKpDLUMXEC9pUBVqUAViUDRbCZDuRFQ0XzgHyQmcVg3clAW3KAuAioU4FB1eCqwUqDzwYnDFYbvDT4g9OsarAZILdUAukiN7Ugnj+Long7wR15QLpEoYMhC68bi5hSGOwALs1E+j2ArAIyBfJEP1lVdM/B1sFqVarGSwyeA10/0KDmwaHgT7IK/uSvDQwNWg2AxcwAgzRgxuTEWakZ2isZxRouzgBI0KDgZpBiUGDWB4mzM4MHgwBDCEAu09wPCM4T3DByZHpnSmPKYCiFImRqgeYQYUwFQJAHehqng=</latexit>(see also Moriyama, Kubo, Furukawa’s slides&Poster)
b H = ⇣ b Q1/2 + b Q−1/2⌘ ⇣ b P 1/2 + b P −1/2⌘
<latexit sha1_base64="AJRuSImHKoCnLtYIHOG/XNRLmvY=">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</latexit>[Aharony-Bergman-Jafferis-Maldacena 2008]
b Q b P = q b P b Q
<latexit sha1_base64="9xBWkbLZxOgSEDpiWJNTaNKejU=">ACk3ichVFNLwNBGH6s7/oqIpG4iKbi1EyRECIRHFwkrao2aXZXYOJ7e7anVZo+gecJQ5OJCLiH7hy8Ac+hPEkcTFwdvthiJ4NzvzvM+8zvPzGi2IVzJWKVBaWxqbmltaw90dHZ19wR7+9Zdq+DoPKlbhuWkNdXlhjB5Ugp8LTtcDWvGTyl7S5W1NF7rjCMtfkgc038uq2KbaErkqicsFIdl9s8h1VluLlDxgrz+3VJXUluWCIRZgXwz9B1Ach+BGzgpfIYhMWdBSQB4cJSdiACpe+DKJgsInbQIk4h5Dw1jnKCJC2QFWcKlRid2ncpizjsybl1Z6up9ZpF4N+h5TDCLMHdsWe2T27Zo/s7deJa9H1csBzVpNy+1cz9Fg4vVfVZ5miZ1P1Z+eJbYw7XkV5N32mOop9Jq+eHjynJhZDZdG2Tl7Iv9nrMJu6QRm8UW/iPVUwToAaLfr/snWB+PRCci4/HJ0PyC/xRtGMIxui+pzCPZcSQpH2PcYNb3CkDyqyoCzVSpUGX9OPL6GsvANd+J1Q</latexit>[Honda, Moriyama, 2014]
3
b H = h⇣ Q1/2 + Q−1/2⌘ ⇣ P 1/2 + P −1/2⌘i2
<latexit sha1_base64="/h01glb193CpEtEnr7M8lsf9ZLU=">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</latexit>(see also Moriyama, Kubo, Furukawa’s slides&Poster)
b H = ⇣ b Q1/2 + b Q−1/2⌘ ⇣ b P 1/2 + b P −1/2⌘
<latexit sha1_base64="AJRuSImHKoCnLtYIHOG/XNRLmvY=">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</latexit>[Aharony-Bergman-Jafferis-Maldacena 2008]
b Q b P = q b P b Q
<latexit sha1_base64="9xBWkbLZxOgSEDpiWJNTaNKejU=">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</latexit>b H α = e3e4 b Q−1 b P − (e3 + e4) b P + b Q b P − h−1
2 e3e4(e5 + e6) b
Q−1 + E α − (e−1
1
+ e−1
2 ) b
Q + h2
1(e1e2e7e8)−1 b
Q−1 b P −1 − h1(e1e2)−1(e−1
7
+ e−1
8 ) b
P −1 + (e1e2)−1 b Q b P −1
<latexit sha1_base64="Nr0moXM5agr2hY65PrckFqOrgD8=">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</latexit>Q = 0
<latexit sha1_base64="yGfdQ7nKLWgcKHYQb9v8obTzXYE=">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</latexit>P = 0
<latexit sha1_base64="SghZGm+O9CFYiRz2Wz8Of5NzvrE=">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</latexit>P = ∞
<latexit sha1_base64="Q4CsTvk7z0dAg62Av3h2DtR/w=">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</latexit>Q = ∞
<latexit sha1_base64="aszeUDvugaVOIP7JMN3Y1S2YUo=">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</latexit>h1e−1
8
<latexit sha1_base64="LOaFwMATVFhFqDb+qc4ZJs8PGFU=">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</latexit>h1e−1
7
<latexit sha1_base64="1IAgu192M0dYhdGx3z/dZSquUvk=">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</latexit>e−1
2
<latexit sha1_base64="7ia7L8ZIGNrw3aSebl8M3NUI9ro=">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</latexit>e−1
1
<latexit sha1_base64="4mVUrj4zl14frJDRMF/DGuSOkZg=">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</latexit>e6h−1
2
<latexit sha1_base64="vVUeIRsFZ1iO5jFcp1CovUDmr1k=">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</latexit>e5h−1
2
<latexit sha1_base64="+2r0VA8nD78VtKAgPbY5Cgeq3s=">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</latexit>h2
1h2 2 = 8
Y
i=1
ei
<latexit sha1_base64="L2FhP3wQbIhStmMDlQcH5bZQr0=">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</latexit>Kubo-Moriyama-Nosaka(2018)
b H α = e3e4 b Q−1 b P − (e3 + e4) b P + b Q b P − h−1
2 e3e4(e5 + e6) b
Q−1 + E α − (e−1
1
+ e−1
2 ) b
Q + h2
1(e1e2e7e8)−1 b
Q−1 b P −1 − h1(e1e2)−1(e−1
7
+ e−1
8 ) b
P −1 + (e1e2)−1 b Q b P −1
<latexit sha1_base64="Nr0moXM5agr2hY65PrckFqOrgD8=">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</latexit>( b P, b Q) ∼ (A b P, B b Q)
<latexit sha1_base64="18LEiGQ2SNK91T+4kJPq2C7Ujs=">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</latexit>h2
1h2 2 = 8
Y
i=1
ei
<latexit sha1_base64="L2FhP3wQbIhStmMDlQcH5bZQr0=">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</latexit>Kubo-Moriyama-Nosaka(2018)
P[X] = Ψ[q−1X] Ψ[X] , b QΨ[X] = XΨ[X]
<latexit sha1_base64="9AkIXw7qc58hj5g31SHqiLGYG+U=">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</latexit>" b H α + z α # Ψ[X] = 0
<latexit sha1_base64="hD1DCXwinDlpgC3fE0RaleswJ3I=">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</latexit>A2 α2q−1 = e3 e1 + h1 e1 + h1e3 e1 + e3e5 h
2 2
+ e3e5 h1h
2 2
+ e2
3e5
h1h
2 2
+ e3 h2 + e3 h2e1 + e3e5 h2 + e3e5 h2e1
<latexit sha1_base64="LOjc5BFqX6eDOYw6GBf6xhB2jws=">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</latexit>i , ¯
i ) = χ10(ei, ¯
A2 α2q−1 = e3 e1 + h1 e1 + h1e3 e1 + e3e5 h
2 2
+ e3e5 h1h
2 2
+ e2
3e5
h1h
2 2
+ e3 h2 + e3 h2e1 + e3e5 h2 + e3e5 h2e1
<latexit sha1_base64="LOjc5BFqX6eDOYw6GBf6xhB2jws=">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</latexit>Kubo-Moriyama- Nosaka(2018)
s2 : (e1, e3, e5, ¯ h1, ¯ h2, α) 7! ✓ e1, 1 e3 , e5, ¯ h1 e3 , ¯ h2, e3α ◆
<latexit sha1_base64="QANBRzwsE25ZSBxGo+zM0gW9LCw=">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</latexit>A2 α2q−1 = e3 e1 + h1 e1 + h1e3 e1 + e3e5 h
2 2
+ e3e5 h1h
2 2
+ e2
3e5
h1h
2 2
+ e3 h2 + e3 h2e1 + e3e5 h2 + e3e5 h2e1
<latexit sha1_base64="LOjc5BFqX6eDOYw6GBf6xhB2jws=">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</latexit>Kubo-Moriyama- Nosaka(2018)
A2 α2q−1 = e3 e1 + h1 e1 + h1e3 e1 + e3e5 h
2 2
+ e3e5 h1h
2 2
+ e2
3e5
h1h
2 2
+ e3 h2 + e3 h2e1 + e3e5 h2 + e3e5 h2e1
<latexit sha1_base64="LOjc5BFqX6eDOYw6GBf6xhB2jws=">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</latexit>2
1
3
5
<latexit sha1_base64="Yv2x0wTxEpatn2SQa0dM8xzr6A=">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</latexit>A2 = √e1√e5 ¯ h2 + ¯ h2 √e1√e5 + √e1√e5 ¯ h1¯ h2 + ¯ h1¯ h2 √e1√e5 √e1e3√e5 ¯ h1¯ h2 + ¯ h1¯ h2 √e1e3√e5 + √e1 √e5 + 1 √e1√e5 + √e1 √e5 + √e5 √e1
<latexit sha1_base64="TkJgGx9U0zF1cLzeVHQEZVe/tZo=">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</latexit>Kubo-Moriyama- Nosaka(2018)
[Hatsuda-Marino-Moriyama-Okuyama(2013)]
ΠA (z, ~) ∼
∞
X
l=1
(−1)l+1Alz−l
<latexit sha1_base64="vkW0Uhre3ySY5gUqkHxDatgXN8Q=">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</latexit>A4 3 3 2χ54 + 5 2χ45 + 11 2 χ1
<latexit sha1_base64="zZjDK9zHXxD9krZ+BFA49/sVgPc=">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</latexit>j≦n
∞
l=1
A1 = 0 A2 = χ10 A3 = (q1/2 + q−1/2)χ16 A4 =
χ1 + ⇣ q3/2 + q−3/2⌘ (χ45 + 3χ1) + 3χ54 + 5χ45 + 11χ1 2
<latexit sha1_base64="50/tx1HCoNk65968pNcQIivwuTE=">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</latexit>log z ∼ −A1z−1
eff +
1
eff −
✓ A3 − 3A1A2 + 3 2A3
1
◆ z−3
eff
+ ✓ A4 − 2A2
2 − 4A1A3 − 8A2 1A2 − 8
3A4
1
◆ z−4
eff + ...
<latexit sha1_base64="Z2PNn2H+aw1Cumg+kA018wI+tVc=">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</latexit>= ✏1(q, ei, ¯ hi) = −✏2(q, ei, ¯ hi) + ✏1(q2, e2
i , ¯
h2
i )
2 = ✏3(q, ei, ¯ hi) + ✏1(q3, e3
i , ¯
h3
i )
3 = −✏4(q, ei, ¯ hi) + ✏2(q2, e2
i , ¯
h2
i )
2 + ✏1(q4, e4
i , ¯
h4
i )
4
<latexit sha1_base64="X1POhG9JiUE9J3AlvE8c8LxS1HY=">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</latexit>log z ∼ −A1z−1
eff +
1
eff −
✓ A3 − 3A1A2 + 3 2A3
1
◆ z−3
eff
+ ✓ A4 − 2A2
2 − 4A1A3 − 8A2 1A2 − 8
3A4
1
◆ z−4
eff + ...
<latexit sha1_base64="Z2PNn2H+aw1Cumg+kA018wI+tVc=">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</latexit>✏1 = 0, − ✏2 = 10, ✏3 = ⇣ q1/2 + q−1/2⌘ 16 , −✏4 =
1 +
(45 + 31) + 41
<latexit sha1_base64="ifLiWrHsc98J603kMnCFX20tBdc=">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</latexit>∞
l=1
log z ∼ −A1z−1
eff +
1
eff −
✓ A3 − 3A1A2 + 3 2A3
1
◆ z−3
eff
+ ✓ A4 − 2A2
2 − 4A1A3 − 8A2 1A2 − 8
3A4
1
◆ z−4
eff + ...
<latexit sha1_base64="Z2PNn2H+aw1Cumg+kA018wI+tVc=">ADaXichVHLbtNAFL2OeRTzaFI2FWxGRI2Koljh0TEqoUNyz5IW6luLNuMU1O/ZE+iNpZ/gBU7BKxAQgjxGWz4ARb9BNRlkdiw4PpR8YgKY9lz58w57x2LHvpZzSY6EhXrh46fLcFenqtes35putha0GicOGziRHyU7tpUy3wvZgHvcZztxwqzA9tm2fCw2N+esCT1ovAxP4rZXmCNQs/1HIsjZLYE0fCjEZmSjpF6AZF6ZNVUyNTMiMJCHPdPB9mPSUnXWL4zOXLq6ZKStJQJUbijfb53Rm6mku9io1EDelaYVo0cVNLCfT8kzNSxftdxeDs0OendlouWQYUqd71lhHJ7WwGRYRdFKZFv79OlAVrmrRz7FLievnt9DzrizLZrNZVoOMlsodGeqxFzfdgwBOIwIExBMAgBI61Dxak+OyCAhRixPYgQyzByiv3GeQgoXaMLIYMC9ED/I5wtVujIa4Lz7RUO9jFxzdBJYEl+oV+oKf0M/1Iv9If53plpUeR5Qhnu9Ky2Jx/trj5/b+qAGcO+79U/8zMwYV+mdXD7HGJFKdwKv1k+uJ08/7GUtahb+kJ5n9Dj+knPE4+ea8W2cbr0HC1D+/t2zxZYqK5qsruvtlQf1VczBbgDy/i/78EKPI1GIAjPBWeCy+FV40TsSUuircqakOoNTfhjyG2fwKuXtnN</latexit>✏1 = 0, −✏2 = 10, ✏3 = (q
1 2 + q− 1 2 )16,
−✏4 = (q2 + q−2)1 + (q + q−1)(45 + 31) + 41, ✏5 = (q
5 2 + q− 5 2 )16 + (q 3 2 + q− 3 2 )(144 + 316) + (q 1 2 + q− 1 2 )316,
<latexit sha1_base64="Oq1O2v3Xl3Vw6EBsQYElEAw/E=">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</latexit>∞
l=1
∼
∞
X
l=1
@X
n|l
(−1)n✏ l
n (qn, en
i , ¯
hn
i )
n 1 A z−l
eff
<latexit sha1_base64="QK78FLf2e3gndXlpVtSxs8qGTQ=">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</latexit>[Moriyama-Nosaka-Yano(2017)]
✏1 = 0, −✏2 = 10, ✏3 = (q
1 2 + q− 1 2 )16,
−✏4 = (q2 + q−2)1 + (q + q−1)(45 + 31) + 41, ✏5 = (q
5 2 + q− 5 2 )16 + (q 3 2 + q− 3 2 )(144 + 316) + (q 1 2 + q− 1 2 )316,
<latexit sha1_base64="Oq1O2v3Xl3Vw6EBsQYElEAw/E=">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</latexit>✏7 = (q
11 2 + q− 11 2 )16 + (q 9 2 + q− 9 2 )(144 + 416) + (q 7 2 + q− 7 2 )(560 + 4144 + 1316)
+ (q
5 2 + q− 5 2 )(720 + 4560 + 9144 + 2516) + (q 3 2 + q− 3 2 )(3560 + 8144 + 2716)
+ (q
1 2 + q− 1 2 )(720 + 3560 + 9144 + 2716),
<latexit sha1_base64="XzmIrHcwnMeVSeA+O3rl1kye0=">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</latexit>✏7 = 11
2 16 + 9 2 (144 + 316) + 7 2 (560 + 3144 + 916)
+ 5
2 (720 + 3560 + 5144 + 1216) + 3 2 (−720 − 560 − 144 + 216)
+ 1
2 (720 + 144),
<latexit sha1_base64="5zyXyqh/KGSufkW0r0aQbyZb34=">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</latexit>SU(2) character
✏4 =
1 +
(45 + 31) + (−54 + 45 + 31)
<latexit sha1_base64="v8Ma8w7j6eAJyJfLc9r5DfFg804=">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</latexit>j≦n
(e1, e3, e5, ¯ h1, ¯ h2) = (1, 1, 1, q, q−1) = (q−1/2, q1/2, q−1/2, q, q−1)
<latexit sha1_base64="1o4lHbmn9xrHBhAHgtFtF8VGJM=">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</latexit>∞
N=0
Partition fn. of N M2-branes
from [Kubo,Moriyama,Nosaka(2018)]
Q = 0
<latexit sha1_base64="yGfdQ7nKLWgcKHYQb9v8obTzXYE=">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</latexit>P = 0
<latexit sha1_base64="SghZGm+O9CFYiRz2Wz8Of5NzvrE=">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</latexit>P = ∞
<latexit sha1_base64="Q4CsTvk7z0dAg62Av3h2DtR/w=">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</latexit>Q = ∞
<latexit sha1_base64="aszeUDvugaVOIP7JMN3Y1S2YUo=">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</latexit>h1e−1
8
<latexit sha1_base64="LOaFwMATVFhFqDb+qc4ZJs8PGFU=">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</latexit>h1e−1
7
<latexit sha1_base64="1IAgu192M0dYhdGx3z/dZSquUvk=">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</latexit>e−1
2
<latexit sha1_base64="7ia7L8ZIGNrw3aSebl8M3NUI9ro=">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</latexit>e−1
1
<latexit sha1_base64="4mVUrj4zl14frJDRMF/DGuSOkZg=">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</latexit>e6h−1
2
<latexit sha1_base64="vVUeIRsFZ1iO5jFcp1CovUDmr1k=">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</latexit>e5h−1
2
<latexit sha1_base64="+2r0VA8nD78VtKAgPbY5Cgeq3s=">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</latexit>